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Could Consciousness Forge the Universe?
Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.

Much of modern theoretical physics assumes that the true nature of reality is mathematics. This is a great mistake. The assumption underlies most of the paradoxes of quantum mechanics, and has no empirical justification. Accepting that the assumption is wrong will allow physics and mathematics to progress as distinct disciplines.

Author Bio

Roger Schlafly has a BSE from Princeton U, and a PhD in Mathematics from U California Berkeley, under I. Singer. He blogs at DarkBuzz.com.

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference."

In fact, in 1887 (the ad hoc length contraction hypothesis is not yet introduced) the Michelson-Morley experiment shows just the opposite - that the speed of light varies in different frames of reference as predicted by Newton's emission theory of light:

http://www.pitt.edu/~jdnorton/papers/companion.doc

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Roger: "The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference." "

Pentcho: "In fact, in 1887 (the ad hoc length contraction hypothesis is not yet introduced) the Michelson-Morley experiment shows just the opposite - that the speed of light varies in different frames of reference as predicted by Newton's emission theory of light: ..."

How did it do that? I have seen the quotes. I am not asking for more of the same. I stopped trying to check your references months ago. I am asking if you will explain in your words how the Michelson-Morley experiment shows ... that the speed of light varies in different frams of references ... ?

It is true that Einstein did not appreciate the Michelson-Morley experiment, as explained in those papers. But the experiment was crucial to Lorentz in 1895, and crucial to many other physicists as evidence for special relativity.

Pentcho Valev replied on Jun. 15, 2012 @ 22:10 GMT

Below is the original calculation based on the assumption that the speed of light is independent of the motion of the light source:

http://www.berkeleyscience.com/relativity.htm

"Michelson and Morley designed an experiment to detect the ether and measure its influence on the speed of light. (...) Let's do the math. Assume light travels at a constant velocity c in the ether. Suppose the apparatus is moving through the stationary ether with velocity v. In the direction of motion, the time for the light to reach the mirror and come back is T=L/(c-v)+L/(c+v). In the direction perpendicular to the motion, the time to reach the mirror and come back is calculated by solving (cT)^2=L^2+(vT)^2, so T=(L^2/(c^2-v^2))^(1/2). The experimental results did not match this calculation. Instead T was the same for both directions (T=2L/c )."

Alternatively, one can assume that, in accordance with Newton's emission theory of light, the velocity of the light, as measured by the observer, is c±v, where v is the velocity of the light source. Suppose the apparatus passes the observer with velocity v. In the direction of motion, the time for the light to reach the mirror and come back is T=L/c+L/c=2L/c. In the direction perpendicular to the motion, the time to reach the mirror and come back is calculated by solving (c^2+v^2)T^2=L^2+(vT)^2, so T=2L/c. The experimental results did match this calculation (for both directions T=2L/c).

Conclusion: In 1887 the Michelson-Morley experiment unequivocally proved that the speed of the light is c'=c±v, as predicted by Newton's emission theory of light, and refuted the assumption that the speed of light is independent of the motion of the light source.

You said: "Suppose the apparatus passes the observer with velocity v. ..."

Please find another thread to respond and I will pursue this at least until I am clear about the value of what you are claiming. If you respond here, even though I appreciate that you did respond, I will not follow up here.

What apparatus passes the observer with velocity v? Also:

You said: "Conclusion: In 1887 the Michelson-Morley experiment unequivocally proved that the speed of the light is c'=c±v, as predicted by Newton's emission theory of light, and refuted the assumption that the speed of light is independent of the motion of the light source."

How did the experiment show that :...it refuted the assumption that the speed of light is independent of the motion of the light source."?

I guess this seems clear to you but it is not clear to me.The experiment showed null results and the follow-up experiments showed null results. How can you say anything more than that the experiment showed that 90 degrees between tubes showed no difference in the local speed of light? The followup experiments say the same. I am asking these question strictly with regard to the empirical results. Thank you.

Michelson 1881: “The result of the hypothesis of a stationary ether is thus shown to be incorrect…This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest”

Michelson 1881: “The result of the hypothesis of a stationary ether is thus shown to be incorrect…This conclusion directly contradicts the explanation of the phenomenon of aberration which has been hitherto generally accepted, and which presupposes that the earth moves through the ether, the latter remaining at rest”

Michelson & Morley 1886: “The result of this work is therefore that the result announced by Fizeau is essentially correct; and that the luminiferous ether is entirely unaffected by the motion of the matter which it permeates”

Now, in 1892 (not 1895), Lorentz writes: “I have sought a long time to explain this experiment [M&M] without success, and eventually I found only one way to reconcile the result with Fresnel’s theory. It consists of the assumption, that the line joining two points of a solid body doesn't conserve its length, when it is once in motion parallel to the direction of motion of Earth, and afterwards it is brought normal to it…Such a change in length of the arms in Michelson’s first experiment, and in the size of the stone plate in the second, is really not inconceivable as it seems to me…Anyway, it seems undeniable that changes of the molecular forces and consequently of the body's size of order of 1 - p2/2V2 are possible. Michelson’s experiment thus loses its verification power for the question at which it was aimed. If one assumes the theory of Fresnel, then its meaning rather lies in the fact, that we can learn something about the change of dimensions”.

By 1895 Lorentz is writing: “Thus we see, that the phase difference expected by the theory could also arise, when (during the rotation of the apparatus) sometimes one, sometimes the other arm would have the greater length. From that if follows, that they can be compensated by opposite variations of the dimensions…If we assume, that the arm lying in the direction of Earth's motion, is shorter by p2/2V2… than the other one, and simultaneously the translation would have an influence which follows from Fresnel’s theory, then the result of Michelson's experiment is fully explained… Consequently we have to imagine, that the motion of a rigid body, e.g. a brass rod or of the stone plate used in later experiments, would have an influence on the dimensions throughout the aether, which, depending on the orientation of the body with respect to the direction of motion, is different… As regards the experimental confirmation, it is to be noticed at first, that the relevant elongations and contractions are extremely small… it would cause a contraction in the direction of motion in the ratio of 1 to √(1-p2/V2). In reality the molecules of a body are not at rest, but there exists a stationary motion in every "equilibrium state".

With the important proviso: “When I developed the present theory, I hoped at first to be able to explain this difference, but soon I found myself disappointed in my expectation” & “Everything taken together, the question is forced upon us, whether it might be possible to adapt the theory to observations, without ceasing to explain the other phenomena discussed in this work. I haven't succeeded in this, and I must therefore leave the whole question open, in the hope that others might overcome the difficulties that still exist”.

The original argument is about the constitution and effect of ether. Correct assumptions about light, ie its independence and constancy, were already in place because this was the basis upon which the result of the M & M experiment was considered. Leading to the conclusion that it proved that matter had a certain ‘elasticity’. The calibration of light speed (ie its speed wrt) will of course vary depending on the reference point. Lorentz dissasociates ether from having any effect, eventually. At first (as above 1892) he hypothesises the actual physical alteration of matter as a function of ether. But that becomes problematical (see above). By 1899 he is trying to resolve the problem (of differential movemnt and an associated effect on dimension) with “such small differences” having the “same local time”. Under pressure from Poincare to ‘propose a coherent theory and not keep adding to the current one’, and bearing in mind his principle “that many electromagnetic actions are entirely independent of the motion of the system”, by 1904 he puts one forward with “The only restriction as regards the velocity will be that it be smaller than that of light”.

Essentially, Lorentz suggests that the alteration in dimension in the line of motion is a function of the flattening of electrons: “I shall now suppose that the electrons, which I take to be spheres of radius R in the state of rest, have their dimensions changed by the effect of a translation, the dimensions in the direction of motion becoming kl times and those in perpendicular direction l times smaller… Our assumption amounts to saying that in an electrostatic system, moving with a velocity, all electrons are flattened ellipsoids with their smaller axes in the direction of motion”.

As Einstein later said (Ether & Relativity 1922): “He [Lorentz] achieved this, the most important advance in the theory of electricity since Maxwell, by taking from ether its mechanical, and from matter its electromagnetic qualities. As in empty space, so too in the interior of material bodies, the ether, and not matter viewed atomistically, was exclusively the seat of electromagnetic fields. According to Lorentz the elementary particles of matter alone are capable of carrying out movements; their electromagnetic activity is entirely confined to the carrying of electric charges.

Light was deemed, correctly, to always start with the same velocity, which will not alter unless impeded in some way. This is obvious, because light is just another entity. Forget that it enables organisms to ‘see’. It results from an atomic interaction (ie always has the same start speed) and, like anything else, will continue to travel at that speed unless acted upon in some way. Furthermore, observation cannot affect reality.

The bottom line here is that, according to the theory, the variable is a quality in matter which results in an alteration in one particular dimension when a differential force is incurred, ie one which also causes it to speed up/slow down. So in the context of comparison, one must be aware of this, because an ‘it’ which is undergoing changing momentum does not have the same dimension as one which is not. It has nothing to do with light, observation, timing and any other spurious explanation which has been alluded to. Of course, whether this dimensional alteration does actually occur, and if so, why and what is its magnitude, are different questions.

Some Platonists argue that mathematics is eternal, exact and perfect – that its truths are discovered by humans rather than invented. A corollary of the Platonist paradigm is that nature is a somewhat imperfect approximation to the eternal mathematical truths. Although many are swayed by these arguments, it is possible that the Platonist philosophy has things backwards.

An alternative paradigm asserts that it is nature that is an eternal magnificent perfection, and that pure mathematics is an inherently abstract and imperfect enterprise. According to this alternative philosophy, when mathematics is applied to modeling nature, the analytical models are:

(1) Artificial (in the non-pejorative sense of the word, and more in the sense that the models are invented rather than discovered), and

(2) Approximate (in the sense that they cannot in principle provide a complete representation of nature’s infinite complexity).

The Platonist paradigm seems to be motivated by a fervent hope that mathematics offers exact answers and absolute truths. Unfortunately, it seems more likely that such things as exact answers and absolute truths will always remain beyond human reach. Perfect circles and absolute certainty probably exist only in the “world” of the imagination. We would do well to be mindful of the distinction between what is real and what is an abstraction.

Mathematics is a truly sublime subject of study and it plays an extremely important role in modeling nature. Yet perhaps applied mathematics is significantly more limited than the Platonists and the Bourbaki physicists are willing to acknowledge.

I just read your essay and have a couple of questions: If mathematics is not a faithful representation of reality, is there any other way to obtain such a representation, or are we forever doomed to ignorance about what "really goes on" in the world, according to your view? Also, can you give an example in which you see physics progressing independent from mathematics?

I say that it is a mistake to equate ignorance with not having a mathematical representation. Physics is what is really going on, not mathematics. We are not ignorant of the physics, as we have many great theories.

Paul Reed replied on Jun. 17, 2012 @ 06:10 GMT

Roger

The real point here is that mathematics is a representational device. And actually it is better, as such, than graphics or words, because it is more specific and has more opportunities for abstract construction. But, it must reflect how reality occurs. Otherwise, it is no more than a belief, ie it has intrinsic validity, but is extrinsically invalid. You allude to a number of flaws in presumptions about how reality occurs, which is the real problem.

As Einstein said "imagination is more important than knowledge". Same as if you have a big imagination and you are a writer and know language and letters well, you can build very fascinating and beautiful novels, stories, and poems. Same as in physics, if you have big imagination and you know mathematics well, you can describe and understand how the natural laws are working. Math is the language of the natural laws in physics. All of us know the language, letters and math, but we don't have an imagination like Shakespeare,Picasso, Einstein, Heisenberg or Newton.

accepted the premise that reality had to be one or the other, and no one admitted the possibility that it might be neither because both are mathematical.”

Though your quote is generally true, it is not entirely true. Specific to my FQXi 2011 Contest Essay, “A World Without Quanta?” (http://www.fqxi.org/community/forum/topic/908) below are some quotes to the contrary …

“To the question, “Is the Universe Continuous or Discrete? ”, we argue that we cannot know 'what is' and strike a philosophical balance and answer, “it is neither and both”.”

“I believe that mathematical models of 'what is' -- as with past metaphysical attempts -- are a never ending search getting us deeper and deeper into the 'rabbit's hole' [Ref. 15]. Physics reduces to Mathematics not through mathematical models but through mathematical identities that describe measurement, which is the essence of Physics. Though Mathematics provides logical certainties, it can not provide the Truth of 'what is'.”

“Is the Universe continuous or discrete? In my humble opinion this is a false dichotomy. It presents us with an impossible choice between two absolute views. And as it is always the case, making one side absolute leads to endless fabrications denying the opposite side. The Universe is neither continuous nor discrete because the Universe is both continuous and discrete. Our 'view' of the Universe is not the Universe. The Universe simply 'is'. “

“So how are we to reconcile continuous vs. discrete? We can begin by being humble enough to acknowledge the hubris of knowing what is the Universe. Since we are limited by our measurements, we should consider these as the beginning and end of all our intellectual efforts in Physics.”

“Mathematics is a tool. It is a language of objective reasoning. But mathematical 'truths' are always 'conditional'. They depend on our presuppositions and our premises. They also depend, in my opinion, on the mental views we use to think. We phrase our explanations the same as we frame our experiments”

“We can have beautiful mathematical results based on any view of the Universe we have. Ask the Ptolemy with their epicycles! But if the view leads to physical explanations which are counter-intuitive and defy common sense, or become too abstract and too removed from life and not supported by life, than we must not confuse mathematical deductions with physical realism. Rather, we should change our view! And just as we can write bad literature using good English, we can also write bad physics using good math. In either case we do not fault the language for the story. We can't fault Math for the failings of Physics.”

“The failure of Modern Physics is in not providing us with 'physical explanations' that make sense. A 'physical view' that is consistent and confluent with our experiences. That will not put us at odds with ourselves, with our understanding of our world and our lives. Math may not be adequate. Sense may be a better guide.”

This paper has done little to convince me that mathematics is not an essential truth that can describe how the universe works at a fundamental level. In philosophy there is something known as the quine-putnam indispensability argument, which states that because mathematics is necessary in order to describe aspects of nature, it follows that is must have an objective existence. In the paper you write that the uncertainty principle undermines mathematics, but there is no evidence for that at all. In fact, there is something known as the "symplectic camel," formulated by Maurice de Gosson, that describes the uncertainty principle in geometrical terms. In addition, the discovery of things in pure mathematics, such as Lie groups, that have found applications in physics many years after they were discovered also lends credence to the idea that we are not simply inventing things at will in mathematics. There is a structure to the entire body of math that is discovered, only our notations and symbols for math are invented. I find this article wanting, and I think that trying to rid mathematics from its place in describing the world is something that will never be successful. Mathematics, in a deep sense, is truth.

I think that you are misunderstood the paper. I am not denying that there is a structure to math, or that math is real, or that math is an essential truth. I have no quarrel with the Quine-Putnam indispensability argument or the symplectic camel. I do not write that the uncertainty principle undermines mathematics. I am not trying to rid mathematics from its place in describing the world. Math is very useful in physics and other sciences.

J. C. N. Smith wrote on Jun. 20, 2012 @ 22:05 GMT

Roger,

Thanks for an interesting essay. I think we share some similar ideas about the relationship between mathematics and objective reality. Following is a quote from my essay, Rethinking a Key Assumption About the Nature of Time: ". . . please don't confuse what are mathematical descriptions of reality with the underlying objective reality itself."

Yes, I see you wrote that in response to someone else saying not to "confuse language with reality". I agree that a description can be different from reality, as the ancient Greeks realized. Your paper mainly challenges the sufficiency of the operational definition of time. I would just add that the definition is entirely due to H. Poincare, as explained in the Wikipedia article on synchronization. He introduced it to relativity theory.

Paul Reed replied on Jun. 21, 2012 @ 05:41 GMT

JCN/Roger

But the differences can only be about 'detail', because no representational technique (and maths is the best one) can replicate all the intricacies of reality. In terms of logic, the essential mathematical components and relationships must correspond to how reality occurs and physically existent entities. Otherwise, it is just a belief system, ie it has no extrinsic validity as a representational model of reality. The fact that the maths 'works', internally, is irrelevant.

Paul

PS: yes Poincare was the essential source of the problem with his flawed concept of time and timing.

"Your paper mainly challenges the sufficiency of the operational definition of time. I would just add that the definition is entirely due to H. Poincare, as explained in the Wikipedia article on synchronization."

You're correct that my challenge is to the sufficiency of the operational definition, but the operational definition far predates Poincare and relativity. In fact, I'd say it dates back to the invention of the first clock. It's deeply ingrained into our thinking and psyches, and therefore not easy to alter or augment, as I believe will be necessary if we are to move forward.

Yes, I totally agree with your opening sentence! The last FQXi contest of "Is Reality Digital or Analog" is also relevant to your essay. My entry featured the imagery of the creation of structure from the starting point of a void. You may find it a useful read. Cheers

Roger if I have missed the point of your paper then I apologize, but if you could help me understand what the overarching theme of the paper is that would be greatly appreciated. Your response to my comments states that you dont deny mathematics is real or useful, and I believe it. But if its true what is the paper trying to get at? If mathematics is real, and if mathematics is essential for describing patterns and phenomena in the objective world, then how on earth does it not follow that at some deep level the universe is in a sense mathematical? And all these comments I keep seeing about "math is only a representation that can't describe everything" or "don't confuse the mathematical representation with reality itself" are a bid confusing. We represent atoms with words like electron, wavefunction, protons, quarks, QCD. Those words represent objects, but those objects have an objective existence. In a similar vein, Schrodinger's equation represents the patterns and observations seen in the quantum world, and those patterns actually exist! Max Tegmark talks about the mathematical universe hypothesis, and at first it might seem a bit crazy that all that actually exists is mathematics. But think about it at a fundamental level, we say things might be made of string and that there are all sorts of dimensions rolled up, or its loop quantum gravity (pick any proposed theory of everything). When you get down to the bottom of it, what the hell is the string made of? Whats this Calabi-Yau manifold all curled up in 6 dimensions? At the most fundamental level, it all boils down to mathematics. And even though it is a deeply mysterious and wonderful thing, you don't need to throw in mysticism or God (feel free to if that's your belief though). We have a multitude of evidence already in the countless mathematical relations and patterns seen in nature. The universe has been hinting at its fundamental language, and it is mathematical.

Pete, I do believe that mathematics is real, but my essay is about physics, not philosophy of math. My point is like the above succinct comment, "the map is not the territory". Yes, the map is real, and the territory is real, but they are not the same.

You mention string theory, and say "At the most fundamental level, it all boils down to mathematics." I say that is a faulty premise of string theory. No one has any way of observing those Calabi-Yau manifolds. Those manifolds are part of a fanciful, desperate, and misguided attempt to salvage a faith in a faulty premise.

Yes, there are mathematical patterns seen in nature. You could regard these as hints that the universe is fundamentally math. Nearly everyone accepts that premise, and agrees with you. The purpose of my essay is to point out that there are also hints that the universe is NOT fundamentally math, and to argue that the premise is wrong. I fully realize that I am going against conventional wisdom.

Pete replied on Jun. 22, 2012 @ 15:16 GMT

Alright I think I understand, you're trying to play devil's advocate in a sense. As you have a mathematical background and think that mathematics exists, would you say that the mathematical universe and the physical universe are two real but distinct entities. I know I'm delving into philosophy a bit and your paper is about physics, but I just wanted to understand your metaphysical worldview. Do the two realities interact at all or are they mutually exclusive?

Mathematics is a language to express the universal truth, so is science of theoritical physics (SR, GR, Quantum mechanics) and spirituality. One can arrive at the universal truth with in one self, the path chosen is not important and all paths are equal to the one who has attained the singularity.

"There are, at present, fundamental problems in theoretical physics...(which)...will require a more drastic revision of our fundamental concepts than any that have gone before. ...these changes will be...beyond the power of human intelligence to get... by...mathematical terms. (and we must try to find and) ...interpret...in terms of physical entities."

I will identify some specific supporting evidence in my own essay. I believe these will show that maths is simply not yet well enough developed to accurately describe nature, and that we are lazy with it, assuming that it's 'abstractions', of 'points and lines' can produce results with REAL physical meaning without bothering to 'renormalise' the abstraction. Is it simply blind faith?

Congratulations on challenging one of the most damaging assumptions in physics.

Thanks for the Dirac quote and the comments, but I very much doubt that Dirac would have agreed with me. The quote is from his 1931 paper proposing anti-electrons and magnetic monopoles on the grounds that they are mathematical possibilities. He argues that advances in physics will come from increasingly abstract mathematics. His approach has been an inspiration to unified field theorists and others who argue that nature is fundamentally mathematical. My essay takes a contrary view.

Peter Jackson replied on Jul. 7, 2012 @ 17:39 GMT

Roger

Are we perhaps too kind to and trusting of maths? A novel view here; http://9gag.com/gag/4689183

Dear Doctor Schlafly, in my essay, Reality Identification, which was published in the 2011 FQXi contest, I did opine that reality had nothing to do with digital or analog mathematical concepts although I did not specify why this should have been so. I have restated that belief in my essay, Sequence Consequence, which has been published in this year’s contest. This is the problem, a symbolic 1 as seen here would have to be minutely different in appearance and physical constitution not only to any other 1 that has ever appeared on this or any other computer, this manifestly singular number 1 would also have to be minutely different from any other number 1 that will appear on any computer screen ever to be built on this or any other planet. This number 1 would have to be different from every other number 1's that have ever been produced or imagined ever. All immutable mathematical laws have been fixed and must be adhered to. Reality has not been completed and it will never be completed. Reality is an ongoing experience. Reality has no shape, no size, and no duration. Your essay was superbly written.

Thanks for your correction. Among those who say that reality is analog, some would say that a physical 1 is minutely different from every other 1 because they are all real numbers that are likely to differ in the 10th decimal place. Your essays make somewhat different arguments.

Joe Fisher replied on Jun. 29, 2012 @ 16:02 GMT

Respectfully Doctor Schiafly, reality is a singular condition that can only occur once. A person cannot measure a singularity by using a plurality of numbers. 1 is only a symbol. The only real Universe occurring once in one place for one eternity should ever be accorded the accurate symbol of 1. Parts of the real Universe and parts of reality can be entertainingly speculated upon by using thoughtful abstract methodology; however, one must never stray from identifying any singularity and try explaining its existence and nature with the forced application of pluralistic insertions. Light is singular. Particles and waves are pluralistic conceptions. There is no way to isolate a single particle or a single wave of light. One can theorize that a certain number of accumulated particles or a certain continuous number of waves ought to cause light to move from place to place, except one has then to assume that all of the accumulated particles and/or all of the waves of light are identical. One has then to assume that the intervening spaces between the quantity of particles and/or the repeatable occurrences of tidal light waves are also identical. All you have to do then is explain how and why light from the sun and from a glow worm and from an incandescent lamp seems to differ so much.

Correct. For any existence to occur physically, and then alter, it can only have one physically existent state at a time. This applies to anything that has physical existence, elementary particle, light, cathedral, you, whatever. Change involves more than one, with the new one replacing the old one. There is no change within any given reality (existent state-a preent).

Change is a singularity. It might only normally be applied to the whole of the Universe. A more correct term would be changing. The Universe stays in one place because all of its integral parts are in motion. The Universe remains stable because all of its integral parts are constantly changing.

What is happening to the universe as a whole we cannot know, because we cannot externalise ourselves to it.

But staying in the reality we can know, change is indeed a singularity. Everything is a singularity. The very nature of physical existence necessitates that. But change involves more than one, because it is the identification of difference, which must involve more than one in order to effect a comparison. So, whilst change occurs one at a time, it is a characteristic concerned with alteration from one to another. It is not an attribute of any given one.

The word we as you are fully aware is a pronoun indicating a state of plurality of you and I, therefore, I agree with you that we could never possibly understand how one Universe could eternally exist once. Perhaps what we could try to do is make a better effort to dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity. For instance, there is a singular motion to the one Universe, but there is no such a thing as speed. In order to measure speed, there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe. While one has to admire how humans have satisfactorily applied numbers to the speed of falling bodies, and motor cars and light, and practically everything else, one cannot help but notice that these numbers keep changing, whereas the one Universe continues to have only one motion. There is certainly one space and one substance distributed throughout one Universe, but space is not distance and substance is not material. Of course there is heat throughout the Universe. But heat is not temperature.

"dissuade the scientific community from knowingly propounding silly laws that supposedly govern all physical activity"

Yep, this is the crux of the problem. Different philosophical takes as to how reality is fundamntally constituted underpin different theories, which is why they have flaws and do not marry up.

I noticed you comment on speed before, and am not sure I agree with it, as written. So let me put it this way. There is movement, which is relative alteration in spatial position. Now, it is relative beause everything must be deemed to be moving. Therefore, in order to calibrate this, one particular example thereof must be selected as a reference (it could be any possible example), otherwise the judgement cannot be effected. Subsequently, this reference must be used consistently to ensure comparability. In simple language, this is no right or wrong answer, only a relative one. The concept of speed is just the relative rate of that movement.

I would certainly not agree with: "there has to be a starting point and there has to be a stoppage point and there are no such points in the continuum of the reality of the Universe", because there obviously must be such points, otherwise there would be no existence. The difficulty comes in identifying them.

Space is an interesting one. It is actually what is not something. There is only something which physically exists, but the 'space' between A & B is only that because of the way in which we have defined A & B. In physical reality, A &/or B may be part of C. And there is something, just not A and B between A & B, but we are not interested in it. Space is just a conceptualisation of the relative size/shape of these somethings. So they can be conceived of as occupying spatial position. So there is intrinsic space, ie the spatial 'footprint' of any given something, or there is extrinsic space, ie that which is not the somethings as defined.

Roger, Typically, the parameters of a physical law concept are identified and then a mathematical algorithm is developed that fits the parameters. The resulting algorithm allows a resultant to be obtained with varying parameters. There is no argument that the mathematical algorithm is artificial relative to the physical law concept, the physical reality. Specific information had to be known before the mathematical algorithm was developed, such as unit sizes and a measured resultant.

The distinction between physical reality and mathematics became a little blurred when a physical law concept was applied to a pair of right triangles and the resultant produced information that was not known to begin with. A paper titled, "A methodology to define physical constants using mathematical constants" was published in the July/August 2011 IEEE Potentials.

Creating a conventional physical law algorithm uses predefined units of measure and a measured resultant. The methodology produced the sizes of the required units of measure and numerical resultants that match the measured physical law. The methodology reveals that properly matching a mathematical technique to a physical law concept provides a better fit to reality, that is, a more faithful representation of nature.

The purpose of vision is to advise of the consequences of touch in time -- per Bishop Berkeley. This has direct, fundamental, relevant, and important significance and meaning when it comes to what are the sensible manifestations (and understandings) of physics. Really think about it.

You packed a lot into 9 pages, Roger! It was a good read. However. I'm curious about something that you didn't mention -- if mathematics is not a faithful language of reality, does that obviate *any* formal representation, e.g., Lev Goldfarb's ETS formalism?

If you get a chance to read it, my essay "The perfect first question" addresses issues that you raise about hidden variables and Bell's theorem.

You refer to Lev Goldfarb. As I understand his approach, it might describe observations or knowledge, but cannot be a true representation of reality.

I see Bell's theorem as just one of many arguments against hidden variables. People want to believe in these hidden variables for some reason, but I say that all the evidence is against the whole concept.

Thomas Howard Ray replied on Jul. 5, 2012 @ 17:03 GMT

The evidence, yes. When the evidence is, however, identical to one's expectation of experimental results, how can one determine that the evidence (data) is a "true" representation of reality? Without a principle of correspondence between a formalized theory and physical experience, we would -- like Mach -- never accept the reality of atoms. Now suppose that atoms are only approximate, sure -- at least, the theory gets us from the naive Bohr orbital model to something more.

Roger, do you agree that science is progressive? If so, what role does language play in that progress? If not, what's the point of doing science?

Yes, I agree that science is progressive. T. Kuhn is famous for saying the opposite, with his paradigm shift theory of science, but he was wrong. Not sure what you mean about language. Sometimes it is useful to have new terminology or language to describe ideas.

Deductive science is not necessarily progressive. It starts with assumptions (axioms) which could be false. For instance, special relativity is based on the assumption that the speed of light is independent of the speed of the emitter. If that is false, not only relativity but modern physics as a whole is 100% degenerate. The following quotation hints at possible falsehood:

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

Pentcho, it does not make any difference whether Eintein thought of light as particles or waves. He was not accounting for the Michelson-Morley experiment, as you point out above, by quoting Norton. His axioms came from Lorentz's work. If you want to understand the progressive nature of those axioms, you have look at the work of Lorentz and Poincare.

Hoffmann is confused where he says, "Einstein resisted the temptation to account for the null result ... and introduced as his second postulate ...". Einstein was not trying to account for the null result. Einstein got the second postulate from Lorentz without explanation. For proof of that, in Einstein's own words, see my blog. So these aspects of Einstein's work are not really relevant to the progress of science.

Thomas Howard Ray replied on Jul. 5, 2012 @ 20:25 GMT

Roger, the reason that I asked, is that if language is independent of meaning -- i.e., if there is direct correspondence between formal descriptions of natural phenomena and the physics as we experience it (Tarski) -- then if language is not primary to discovery, how is one to judge progress?

If the role of language is merely to describe phenomena, so that personal experience is identical to language (I realize that this is the LP view) it follows as well, that experience is substituted for meaning. That being so, it stands to be demonstrated that no meaning can be assigned to a positivist result that is not evident in physical experience.

Does this accurately describe your position? If so, how does one prove within this framework that science is progressive? After all, such a feat must first assume that language is progressive and independent of meaning, and we have arrived at a contradiction.

Einstein was a plagiarist but this is not indeed very relevant to the progress of science. If his 1905 light postulate is true, then special relativity, plagiarized or not, is great. However if the light postulate is false, then "nothing will remain of contemporary physics":

Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."

Clues:

http://arxiv.org/ftp/physics/papers/0101/0101109.pdf

"The two first articles (January and March) establish clearly a discontinuous structure of matter and light. The standard look of Einstein's SR is, on the contrary, essentially based on the continuous conception of the field."

http://www.pbs.org/wgbh/nova/einstein/genius/

"And then, in June, Einstein completes special relativity, which adds a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves."

Thomas, I am not sure I understand your question. When I say that science is progressive I mainly mean that modern science keeps bringing advances like cell-phones and Higgs bosons, that were just not possible with previous levels of science. I also have a positivist philosophy, so I believe that science advances just as facts and knowledge accumulate.

My trouble with the word "language" is people sometimes say that mathematics is a language. But math can prove things as well as describe things. Maybe you could give an example to explain just what you mean.

Thomas Howard Ray replied on Jul. 5, 2012 @ 22:43 GMT

Let me try and put it this way, then. Do you think that cell phones and the Higgs boson were discovered independent of the physical theories that incorporated and predicted them?

Most important, how likely do you think those theories would have been possible without the language that supports them, that makes comprehension possible?

There's no question -- that whatever else mathematics is -- it is a language. This is exceedingly easy to demonstrate, by the mere fact that any mathematical statement (though it is most unnecessary, tedious and impractical) can be translated into natural language.

Einstein's 1905 light postulate had a condition, ie in vacuo. Later this was dropped. That is, in 1905, light is existent in one condition (ie no interaction from anything else) whilst matter is being affected by something else, becasuse there is Lorentz's length contraction on matter. In simple language, not all entities are in the same world at the same time. Note the caveat between the presentation of the two postulates: "only apparently irreconcilable". In other words, 1905 does not equal SR. Indeed, in 1916 when expounding GR, he clearly stated what constituted SR.

Thomas, I would say that physical theories were need for those advances. The language is the easy part. I would not call mathematics a language. Yes, mathematical ideas can be expressed with mathematical symbols. You call use of those symbols a language. But what's the point? Do you call music a language?

Thomas Howard Ray replied on Jul. 6, 2012 @ 09:22 GMT

Roger, of course music is a language -- and like mathematics and natural language itself, also an art. I am reminded that Einstein (an expert violinist) once remarked that a symphony could be described mathematically by variations in sound wave pressure, though that would not capture the meaning of the symphony.

Likewise, Einstein's mathematically complete theory of relativity does not reveal its meaning in the symbols, but in the playing.

Okay, Thomas, call physical theories, mathematics, and music languages if you want. By your definition, something is a language if it can be represented in some other way, with loss of meaning. But then I have to disagree with your earlier premise that "language is independent of meaning".

Paul Reed replied on Jul. 7, 2012 @ 07:12 GMT

Roger/Tom

The whole point of this particular exchange is that whatever representational device is being deployed, it must correspond with phenomemena and their relationships, 'as is' if it is to be a valid representational model. Mathematics is inherently more accurate than language, so it is a better tool for this job. But that does not mean it will be accurate, because that depends on actual correspondence between the model and the actuality being modelled. The model, of itself, cannot create accuracy, just by virtue of being intrinsically valid.

You misunderstand me, Roger. Language is the formalized representation of physical phenomena. That it can be manipulated to produce novel forms doesn't imply meaning, however. Hence my anecdote about Einstein and the symphony.

That language is independent of meaning is what allows us to deduce meaning objectively without capriciously assigning meaning to a phenomenon -- by matching elements of theory one for one to elements of experience. If this were not so, and the world presented itself as no more than "what you see is what you get" -- without, as you say, a faithful formal representation -- all of our knowledge would be based on experience alone, and all our conclusions made inductively without an attempt at objective meaning. As it is, though, nearly all of our scientific/technical knowledge is counterintuitive, deduced from theoretical language and validated in experiment.

Thomas, you say that mathematics and music are languages, and you say that language is independent of meaning. That says that mathematics and music are independent of meaning. I disagree. They have meaning.

Tom, I cannot figure out whether you are saying that math and music have meaning, or do not have meaning. But either way, I have lost track of what this has to do with physics. Maybe you could make your point in a more specific way.

Paul Reed replied on Jul. 8, 2012 @ 05:01 GMT

Tom

“Meaning is abstracted in the correspondence of theory to physical result”

This not so. As Roger wrote, ‘what applies to one applies to the others’. They are all devices which can be used to represent something. The meaning stems from what you decide it will represent. Maths is just less open to interpretation, it is not inherently correct. But for any device to be used properly, ie scientifically, then that meaning will also be that which corresponds with the physical result. The fact that 1+1=2 in the maths system, is irrelevant if it does not in what is being modelled using that system.

What this has to do with physics? It has to do with your claim that "nature has no faithful mathematical representation." I asked if you think, by extension, that nature has no representation in ANY formal language, and you didn't disagree. These formal languages include mathematics and music. Perhaps you mean to say that nature has no COMPLETE representation in a formal language -- in which case you would have to prove that science is not progressive, because language is demonstrably progressive with science. But since you agree that science is progressive, and you obviate any role for formal language in scientific discovery. This is contradictory.

In any case, we seem to talking past one another at this point, so further replies by me may amount to a disruption. So I won't continue. Good luck in the contest.

Tom, I agree that science is progressive. I do not agree that mathematics and music are languages. Science, math, and music cam be described by language, of course. When you say that math and music are languages, you are using some definition of "language" that I do not understand.

Your essay was so refreshing I've had to re-read it. A small issue on your point about last years essays. I flagged up the role of maths and took a wholly ontological approach to expose and overcome a measurement methodology problem in handling 'discrete' kinetics (2020 'Vision'). It was a top 10 finalist but I was disappointed the judges seemed to miss or avoid the important conclusion.

Indeed I strongly applaud your suggestion that relativity is "a theory about something that would be due to our methods of measurement." I'm reasonably sure I've identified a serious misunderstanding about measurement methodology which has broad and deeply fundamental implications (the essay should pop up any time now). I really look forward to your comments.

For now, can you comment on this; As motion is an invalid concept in geometry, and geometry is the basis of vector space, can we assume that motion is validly and adequately described by vector space algebra?

Vector spaces are ideal for describing motion of particles. If the moving particle is really a wave, then the situation is more complicated.

Peter Jackson replied on Jul. 6, 2012 @ 18:39 GMT

Roger

When a photon in a medium interacts with an electron moving laterally (i.e. at the refractive plane of a moving medium), the interaction time is non zero (say 6.5x 10^-24s for c and a classic electron radius) so there must be a 'kinetic' effect from the evolution of interaction. This is consistent with recent findings at a larger scale, i.e. from astronomy (i.e. Emsellem, E., et al., Atlas 3D. MNRAS 414 2. 888-912. June, 2011) which derives a kinetic term for the interaction with halo matter which matches observation (also finding galaxy rotational velocities quite accurately).

Yet Cartesian co-ordinate systems and 'point' particles can't even 'see' any such effect mathematically. When using Propositional Dynamic Logic instead of simple maths an ontology emerges, but this would point at vector space and overlapping inertial 'wire' frames as inadequate to model reality ('time stepping' maths can also do it after a fashion). Could it possibly be so? And would that be just tooo heretical?

This is a specific example of the generic point I have just made above (and have made many times before). It is not the intrinsic validity of the model which ultimately counts (though it is a good start to create one which works in accord with the rules!), but its extrinsic validity vis a vis that which is being modelled.

"[T]he ... fermion minus sign problem ... is often misconcieved as a technical detail frustrating the careers of numerical simulators. It is much more. It is the nightmare of modern physics. At the moment one is dealing with an infinity of interacting fermions, it is a tragic fact that no methodology is available to handle the problem in a systematic, controlled fashion. The standard escapes are to either declare the non-interacting fermion gas to be the universal truth, or to suppose that fermions are completely eaten by collective bosonic fields. The devastating influences of the minus signs are most clearly felt in high Tc superconductivity, the subject of heavy fermions, and adjacent areas like the 2d metal-insulator transition. However, it permeates all of fundamental physics, from the nature of the core of neutron stars up to string theory. When you still think it is a non-existent problem, I am interested to hear your answer to the following simple question: can a state of matter exist, characterized by an irreducible sign problem in the scaling limit (i.e. it cannot be absorbed by an appropriate transformation) which cannot be adiabatically continued to the Fermi-gas?"

I enjoyed reading your essay. It is really clearly written and thoroughly accessible, even to someone without a maths or physics background. You have set out your arguments very clearly and I might have been convinced had I not previously given this subject quite a bit of thought.

You wrote "It is time to accept the non-mathematical nature of reality, just as it was time to accept the non-Euclidean geometry of spacetime when H. Poincare proposed it in 1905." I'm sorry that I must disagree. In my opinion it is not that the universe can not be described mathematically but that the structure of reality has been inadequately comprehended, so that the mathematics when applied are inadequate to describe all of its facets in their correct relationship. That might sound like nonsense but it is explained more methodically in my essay and accompanying diagrams.

I also think that mathematical relationships are inherent to the structures and patterns of the universe and those relationships are also the forces for change. Mathematics "in vivo" is not identical to the mathematics modelling our observed reality. That does not make the unobserved reality non mathematical. This view does open up new possibilities for mathematical representation and new considerations of how numbers and sets relate to a broader view, the physics of the entirety of reality.

Having disagreed with you, I would like to say that there is a lot in your essay that I do like, it is very good, well constructed and thought provoking. Good luck in the competition.

Thanks for your comments. I see your essay argues that space-time is emergent, and does not exist externally. These essays go against conventional wisdom, so I don't expect many people to be convinced.

Georgina Parry replied on Jul. 13, 2012 @ 02:06 GMT

Dear Roger,

I hope that my essay and accompanying explanatory framework diagram do give a convincing argument. However I agree that a quick glance at the list of false assumptions is not in itself convincing at all.It is a pity if people's minds are closed so easily. It is unconventional, I agree, and requires some thought to see how it functions and overcomes so many problems. I have a higher resolution file of diagram 1. if the quality is a problem. I'm not saying I'm right and you are wrong. We are both giving sensible, well reasoned arguments from our own viewpoints, in my opinion. Which argument is ultimately more useful for science time will tell.

If we assume that we live in a universe which creates itself out of nothing, then conservation laws say that everything inside of it, including spacetime itself, has to add to nil.

The universe then is that unique, paradoxical thing which has no physical reality as a whole, no 'exterior', but only exists as seen from within.

The universe therefore isn't only not a mathematical object, it isn't even a physical object.

By treating it as an object which, as a whole, has particular properties even though there's nothing outside of it, nothing with respect to which it can have properties, physicists have made an awful mess of physics.

Quoting your essay, "The most puzzling quantum experiments are the double-slit experiment and the spin measurement of entangled particles. Quantum mechanics predicts these outcomes without difficulty, but these experiments have been described as impossible to understand or as proof that there is no reality."

I'm still writing my paper, but I came to the conclusion that the double-slit experiment makes perfect sense and is perfectly natural, provided that you make one assumption. You have to assume that an aether exists, but not just any aether. You have to assume that an aether made of waves exists, perhaps even probability amplitude waves. In the two slit experiment, a single photon or particle can be fired at the two slits. It's not the particle that interferes, it's the wave-function that describes its pathway. The pathway/quantum wave/aether wave is what interferes, not the particle. The particle only exists as an excitation of the waves of the aether. The aether waves interact with the slits as interfereing waves (no suprise there). The particle is just an excitation of the waves of the aether. The information about which slit it went through just doesn't exist.

If the particles are really waves, then yes, there is nothing confusing about the double-slit experiment.

Jason Wolfe replied on Jul. 13, 2012 @ 05:19 GMT

But I think the physics community might be reluctant to embrace wave phenomena as an aether medium. For one, a lot of people have had the Michelson-Morley drilled into their heads. So now it's more of a reflexive answer: "No there's no aether!" than it is a well contemplated answer.

I think the aether exists and is made out of waves; I call them aether medium waves. Quantum Mechanics describes quantum systems with wave-functions. I modeled my aether medium waves after wave-functions. Wave functions/wave amplitudes are a mathematical description of aether waves.

Wave-functions have eigenstates for position and momentum. Eigenstates for position translate into available space for particles. Aether waves create the properties of the vacuum.

AM waves are the embodiment of the speed of light. I'll explain this better tomorrow.

The physical reality of aether medium waves is that they are subtle and difficult to detect. Wave functions are like fluffy clouds compared to particles which are like airliners.

Photons are excitations of aether waves. Photons and AM waves share a dual causality relationship. Where there are photons, there are also AM waves. Likewise, AM waves make it possible for photons to exist.

Last thing. What does the wave-function of a photon in a strong acceleration field look like?

Here is a picture of a typical physics wave. http://www.google.com/imgres?um=1&hl=en&client=firefox-a&sa=N&rls=org.mozilla:en-US:official&biw=1260&bih=640&tbm=isch&tbnid=QzjfmAsUPbmrDM:&imgrefurl=https://sites.google.com/a/ggwo.org/ggca_science_lab/Home/physics/physics-light-and-optics/physics-waves&docid=UMm9Kh95pRdWjM&imgurl=http://eesc.columbia.edu/courses/ees/slides/climate/wave_props.gif&w=613&h=442&ei=ImcAULGKEMHLqgGai6G-Bw&zoom=1&iact=hc&vpx=171&vpy=183&dur=1234&hovh=191&hovw=264&tx=133&ty=86&sig=109702152363049456989&page=1&tbnh=120&tbnw=166&start=0&ndsp=18&ved=1t:429,r:0,s:0,i:90

My question was as stated, given the concept wave, irrespective of which particlar 'wave', then, generically, what physically constitutes this. The reason I ask this is because I suspect that once wave is so defined, then what one actually finds is a sequence of physically existent states, not 'something'.

It sounds like you're referring to quantum eigenstates. For example, in the hydrogen wave-function, there are 4 quantum numbers (n, l, m_l, m_s). I'm just not sure what you mean by a "sequence of physically existen states, not "something"."

Wave-function are, to some extent, a descrption of aethe waves. The hydrogen wave-function is a representation of the aether form of the atom. Eigenstates for energy level, momentum, position, angular momentum, spin, are all places that an electron can exist in a hydrogen atom. For an aether hydrogen atom, there are available position that that the electron can be (space), there are possible values for momentum, etc.

I'm somewhat in sympathy with Jonathan Burdick's pithy response, but of course in ten pages you do more that say that the map is not the territory. I take you also to say that the territory (reality) is not mathematical. I suppose that as a positivist, albeit I think you are too influenced by the post-positivists to really claim the name, you might accept that Physics is the systematic description of reproducible experimental results. Whatever systematization we use would then seem to be a part of mathematics, which leaves me wondering what principle or postulate you are proposing, or critiquing, to speak to the theme of the competition? [An empirical principle is, I take it by definition, a systematic view of some large body of experience, which to be successful must allow the construction of a tractable mathematics, whereas a postulate is something more in the realms of convention. Interesting that the competition is phrased in terms of postulates rather than principles.]

It is true that there are some parts of Physics that are apparently less systematized --more empirical or phenomenological, one might say-- than other parts, but where there is chaos there is the presumption that a better systematization might be possible if a good enough mathematician comes along. What is left to do is very hard, in the usual story of all the low-hanging fruit having been picked, but we have made better tools than our forebears. It is also possible that there is some part of the territory that only ever happens once, so that it cannot be subject of Physics taken to be a repeatable experimental subject. Indeed, the irreproducibility of quantum mechanical phenomena at the finest level of detail precisely underlies the turn to statistics, where there is reproducibility, and the idealization of statistics as probability.

In any case, there has been a constant interplay between Mathematics and Physics, a "battle" that has recently been going relatively less well for the Platonists, which I think many creative theoretically-inclined Physicists continually renegotiate in their attempts to construct new models, sometimes stepping into high theory, sometimes stepping into phenomenology, anything that helps in the construction of a new systematization of experimental data.

Peter, I like your phrase "construction of a new systematization of experimental data." Yes, that is a laudable goal and mathematics is a terrific tool. I also "accept that Physics is the systematic description of reproducible experimental results."

My purpose is to better understand the limits to mathematical reasoning in physics. For example, consider the No-cloning theorem. If a physical state is perfectly representable by some numbers or other mathematical objects, then it is very hard to understand why a perfect copy cannot be made. Perfect cloning of mathematical objects is axiomatic. I say that the quantum state is great for systematizing experimental data, but when you take it too literally as being reality then paradoxes result. It is better to step back, and admit that our mathematical models may be necessarily imperfect.

Elvira Colburn wrote on Jul. 27, 2012 @ 04:42 GMT

"I will love the light for it shows me the way; yet I will love the darkness for it shows me the stars."- Og Mandino

We keep shining a brighter light ( mathematics ) looking for the stars ( answers ). My interpretation of Roger’s essay is to consider radically revising the approach to answering the big questions about the nature of reality. Could it be as simple as metaphorically turning out the lights to see the stars? The answer is surely that simple, and no doubt all around us. We may be blinded to seeing seeing the answer by the bright light of academic thinking. As the daddy goldfish said to the baby goldfish as they swam in circles around the tiny fishbowl: “ Even though you can’t see it, I assure you water exists”. The great mystery of reality and existence can be torn down to it’s basic components through the language of mathematics, but can only be understood by seeing the deepest truths we are already experiencing by our very existence.

You tackle the assumption that mathematics is always a faithful representation of reality, and find it wanting. As you say, 'hardly anyone distinguishes between scientific realism and some sort of mathematical idealization of the world.' Indeed, physics journal papers are invariably stuffed full of mathematics but devoid of interpretation, and often don’t even show the courtesy of providing a conclusion. Apparently most authors do not see that they have any responsibility to explicitly communicate the implications of their work for interpretation of the natural world. Your essay incisively identifies the tacit premises and underlying mental models that lead to this kind of mathematical idealisation.

As you point out, our current best theory of physics, quantum mechanics, uses mathematics to construct a representation of reality, but is unable to provide a descriptive explanation of reality. You also say that, 'It seems unlikely that mathematical structures would be suitable for a true physical reality.' What structures (or methods) would be, in your opinion?

Thanks for your comments. As I see it, an electron is a physical object, not a mathematical one. We can measure things like position and momentum, but these are not intrinsic properties of the electron. You can use mathematics to describe it, and say that an electron is in a particular orbital or has a particular energy, but it is more mysterious than that. It is not really a particle and we do not even know whether it behaves in a deterministic way.

Saying that an electron is in a particular orbital is a very good description for some purposes. It allows predictions about chemical bonds, for example. So I am not saying that there is no description. I just think that there are limits to what you can do with a mathematical model.

Jayakar Johnson Joseph wrote on Aug. 8, 2012 @ 18:13 GMT

Dear Roger Schlafly,

I think, adaptations of wave mechanics with strings as particles, emerges with faithful mathematical representation that demonstrates the function of group homomorphism for this particles of strings.

An excellent essay which I fully agree with. Math is the map(s) of reality, not the bedrock on which it rests. There is though a further argument that might help to support your point:

What is the function of a map? To isolate out and distill the salient points one wishes to focus on. Necessarily many different maps can be created of the same or adjacent territories; road, topographic, butterfly ranges, algebra, geometry, calculus, QM, GR, etc. Each having their advantages. To paraphrase The Lord of the Rings; Why don't we have a math to rule over all the other maths? and give a complete description of everything?

Because that defies the function of math! Which is to focus, isolate, distill out that particular aspect of reality which best serves the purpose at hand. This goes to the nature of perception. It is inherently subjective. Information tends to cancel out other information. Consider a camera. To get the clearest photograph of an object in motion, we use as short a shutter speed as possible. Yet actually we gather much more light and thus information, if we were to leave the shutter open longer, but the result would blur the image. Not only is information very much a function of perspective, but even the creation and destruction of information is itself information. Can't have your cake and eat it too. There is no God's eye view and a theory of everything is seeking that God's eye view. The problem goes to the concept of God. The absolute is the elemental from which reality rises, not an ideal form from which it fell. Everything and nothing are the same, because everything cancels itself out. The happy medium is a big flatline on the universal heart monitor.

Roger: I appreciate the way you handled quantum mechanics (QM)in your essay. I quote your statement and questions. My position is all explained in my essay, A Challenge to Quantized Absorption by Experiment and Theory.

"It is rare in science for an 80-year-old theory to be so relentlessly challenged by theorists, and yet be so accurately confirmed by experiment."

ER: Until now. My experiments test QM at its most fundamental level, and QM fails. This was all Very difficult to develop.

"Does quantum mechanics have some flaw, or do the challengers have some conceptual misunderstanding?"

ER: Yes to both. The precursor to QM was the loading theory (LT), but it was prematurely rejected. QM will model a wave function associated with a particle. LT is a two state system, a wave state and a particle state. It seemed impossible for an atom to turn into a wave, spread out, and then load up and turn back into a particle. The particle is a contained wave structure. LT needed to be developed to make this picture reasonable, and LT needed to work for our key experiments that led to QM; I did all that. Physicists stopped considering LT because it was given false witness by quantum supporters in our literature and textbooks; I describe all that in detail. My experiments show one gamma-ray can split and cause two gamma detection pulses to appear. I also show one alpha-ray can split and cause two full alphas to appear. By experiment, QM fails and the loading theory works.

"Why are physicists so fond of quoting R.P. Feynman and saying that no one understands quantum mechanics?"

ER: Feynman and quoters understand that by embracing duality, QM is not understandable. Particles cannot cause wave patterns, and waves cannot not magically collapse from everywhere into a particle. They stuck with QM because it worked and there was no experimental challenger. We will only understand QM when we overcome it.

Bob Jones comments on my blog that I've "got the relationship between math and physics all wrong." I replied there.

Jose P. Koshy wrote on Aug. 29, 2012 @ 10:26 GMT

Roger,

I agree with your view. Mathematics cannot be a faithful representation of the physical world. To describe a physical world, we require physical laws, and to explain how the physical world changes we need mathematical laws. This fine distinction between mathematics and physics is often neglected nowadays, and mathematical models having no physical meanings are often brought out as the real representation of physical world.

I dunno - "mathematics" is an awfully big subject, and one can cook up all sorts of ideas that have nothing to do with why the world is the way it is. So ? we already know that. But it appears that we can not really disentangle the Math we need to make sense of phenomena, and Physics. They are not, in any realistic sense, "distinct disciplines" when it comes to subjects like Spin. Physics seems to use only a small part of math - it boxes in the sort of math that is crucial, and leaves open a lot of stuff we can not make sense of - like why it looks like there are 3 generations of fermions. Does anyone really think the explanation is NOT mathematical - probably algebraic ? All the speculation is no surprise - hopefully we learn from mistakes.

When you speak of first principles, it seems to me that we also have been ignoring a first principle which describes the limits of one of our main mathematical tools. I am speaking specifically of the arbitrary constant of integration from anti-differentiation. The human senses are normally only good for determining differences, and not absolute magnitudes. When we anti-differentiate gravitational force, we can certainly map out a gravitational potential but our calculus tools tell us that while F'=gravitational force, there is no way to know if F=f1 or F=C-f2, or any other combination where the spatial derivatives (gradients) are equivalent). We simply chose the simplest. Thus the "map" of reality is only true up to the limits of what our mathematical tools can tell us. I bring this up because the Einstein field equation, using a much more mathematically logical unimodular approach, could easily have the Einstein tensor substituted such that

, which seems a better fit for being able to have a large vacuum energy which appears small.

So this leads me also to the question of choosing which mathematical reality I see from the evidence, and your positivist one strikes the right chord.

I read your essay and found it very interesting and well written. I highly appreciate and share your viewpoint.

Just as any spoken or written language is an indispensable tool for describing and representing physical reality, mathematics as a symbolic logic system is also an extremely valuable tool for representing and analyzing physical reality. In my essay I have written, "Apparently, growing complexity of mathematical models developed to represent physical reality, often obscure the physical reality to such an extent that the difference between the two is lost in the specialist jargon. In the process however, we have lost our intuitive guide, the common sense, to judge whether these abstract representations do really describe physical reality or simply lead us to a world of fantasy".

As you know, with arbitrary assumptions we can build wonderful fantasies. But to come close to building a model of reality, we must use barest minimum of assumptions and such assumptions that are used must be plausible and compatible with physical reality. For this reason I think FQXi has chosen a most appropriate topic for this contest.

You are also requested to read my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion. However, you are welcome to disagree with me regarding my proposal for fundamental research in 'Physical Space' because, possibly, that idea may be still ahead of its time!

You fight Einstein's relativity in a way that will please Einsteinians - you will get many points from them. You wrote:

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference. G. FitzGerald was the first to make the logical deduction from the apparent contradiction, in 1889, by saying, "I would suggest that almost the only hypothesis that can reconcile this opposition is that the length of material bodies changes..." H. Lorentz made a similar deduction..."

Quite the opposite happened. Originally the Michelson-Morley experiment showed that the speed of light varies with the speed of the light source, as predicted by Newton's emission theory of light. However at that time the emission theory was totally forgotten and the ether theory's tenet that the speed of light is independent of the speed of the light source was universally accepted. So FitzGerald and Lorentz had to advance the ad hoc length contraction hypothesis in order to reconcile the ether theory's tenet with the null result of the experiment.

Pentcho, you are correct that the Michelson-Morley experiment could have been interpreted as favoring an emission theory of light. Probably some physicists at the time said exactly that. But most everyone was sold on a wave theory of light, and Michelson-Morley was seen as crucial to Lorentz and others at the time, and in modern textbooks. So yes, Michelson-Morley was the crucial experiment. It is a historical fact that it led to relativity, whether or not it has an alternate interpretation.

Pentcho Valev replied on Sep. 3, 2012 @ 14:49 GMT

Yes, Roger, at the time there were physicists immeasurably cleverer than Einstein. Walther Ritz for instance:

http://www.datasync.com/~rsf1/crit/1908a.htm

Walther Ritz 1908: "The only conclusion which, from then on, seems possible to me, is that ether doesn't exist, or more exactly, that we should renounce use of this representation, that the motion of light is a relative motion...

Yes, Roger, at the time there were physicists immeasurably cleverer than Einstein. Walther Ritz for instance:

http://www.datasync.com/~rsf1/crit/1908a.htm

Walther Ritz 1908: "The only conclusion which, from then on, seems possible to me, is that ether doesn't exist, or more exactly, that we should renounce use of this representation, that the motion of light is a relative motion like all the others, that only relative velocities play a role in the laws of nature; and finally that we should renounce use of partial differential equations and the notion of field, in the measure that this notion introduces absolute motion."

Albert Einstein (1954): "I consider it entirely possible that physics cannot be based upon the field concept, that is on continuous structures. Then nothing will remain of my whole castle in the air, including the theory of gravitation, but also nothing of the rest of contemporary physics."

Clues:

http://arxiv.org/ftp/physics/papers/0101/0101109.pdf

"The two first articles (January and March) establish clearly a discontinuous structure of matter and light. The standard look of Einstein's SR is, on the contrary, essentially based on the continuous conception of the field."

http://www.pbs.org/wgbh/nova/einstein/genius/

"And then, in June, Einstein completes special relativity, which adds a twist to the story: Einstein's March paper treated light as particles, but special relativity sees light as a continuous field of waves."

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

The Einstein biographers and historians (Holton, Stachel, etc.) now say that the Michelson-Morley experiment was of no importance to Einstein, and he might not have even known about it in 1905. Einstein relied on Lorentz's analysis of it. So I say that the experiment was crucial to relativity because it was crucial to FitzGerald, Lorentz, Poincare, and Minkowski. Einstein does not even talk about the importance of it until 1909.

While your views are often at variance with accepted tenets, they largely agree with my own experience, reasoning, and critical analysis of literature.

Inspired by a stunning result of experiments by Feist, Fig. 5 of my essay offers a plausible explanation of why the MMX failed to measure the aether drift. Pentcho did not yet respond.

I have to credit Paul Marmet for making me aware of the key importance of a possible mistake in Potier's correction to Michelson's original calculation: Most likely, this correction was still not yet correct.

Israel Perez claims to reinstate the preferred frame of reference while maintaining Einstein's SR. How do you judge this claim?

Stachel and Norton go as far as to accuse brothers Einsteinians of lying about the Michelson-Morley experiment but assure that Einstein, unlike "later writers", was honest and never cited the experiment as evidence for the principle of the constancy of the speed of light:

Stachel and Norton go as far as to accuse brothers Einsteinians of lying about the Michelson-Morley experiment but assure that Einstein, unlike "later writers", was honest and never cited the experiment as evidence for the principle of the constancy of the speed of light:

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

http://www.amazon.com/Einstein-B-Z-John-Stachel/dp/0817641432

Einstein from 'B' to 'Z', John Stachel, p. 179: "Are there any common features to Einstein's mentions of the Michelson-Morley experiment? Yes: Without exception, it is cited as evidence for the relativity principle, and is never cited as evidence for the principle of the constancy of the velocity of light."

In fact, Einstein devised the lie, as can be seen from the New York Times 1921 article:

The New York Times, April 19, 1921: "The special relativity arose from the question of whether light had an invariable velocity in free space, he [Einstein] said. The velocity of light could only be measured relative to a body or a co-ordinate system. He sketched a co-ordinate system K to which light had a velocity C. Whether the system was in motion or not was the fundamental principle. This has been developed through the researches of Maxwell and Lorentz, the principle of the constancy of the velocity of light having been based on many of their experiments. But did it hold for only one system? he asked. He gave the example of a street and a vehicle moving on that street. If the velocity of light was C for the street was it also C for the vehicle? If a second co-ordinate system K was introduced, moving with the velocity V, did light have the velocity of C here? When the light traveled the system moved with it, so it would appear that light moved slower and the principle apparently did not hold. Many famous experiments had been made on this point. Michelson showed that relative to the moving co-ordinate system K1, the light traveled with the same velocity as relative to K, which is contrary to the above observation. How could this be reconciled? Professor Einstein asked."

In that NY Times article, Einstein is describing how Lorentz explained Michelson-Morley. It really doesn't matter what Einstein's opinion was. If you want to know how we got that explanation, ask Lorentz, not Einstein.

Anonymous replied on Sep. 3, 2012 @ 17:10 GMT

In 1887 the Michelson-Morley experiment UNEQUIVOCALLY confirmed the emission theory's tenet that the speed of light varies with the speed of the light source (c'=c+v) and refuted the ether theory's tenet that the speed of light is independent of the speed of the light source (c'=c). By advancing, ad hoc, his absurd length contraction hypothesis, Lorentz made the experiment confirm the false tenet (c'=c) and refute the true one (c'=c+v). That marked the beginning of the end of rational physics.

An interesting and thought-provoking essay! You write: "It is rare in science for an 80-year-old theory to be so relentlessly challenged by theorists,and yet be so accurately confirmed by experiment. Does quantum mechanics have some flaw, or do the challengers have some conceptual misunderstanding?". I thik both, as can be seen from my own essay. However I will not recommend you to read it. Better, if you haven't already read Robert H. McEachern's essay "Misinterpreting Reality: Confusing Mathematics for Phisics" I strongly recommend you to do so.

"The idea was described by the ancient Greek philosopher Socrates in about 400 BC, and written by Plato as the Allegory of the Cave. People in the cave see shadows, and do not appreciate the 3-D nature of the objects causing the shadows. They are seeing a 2-D projection of 3-D objects.

A photograph is also a 2-D projection of a 3-D scene. A measurement with a meter stick is a 1-D projection. Other observations can also be viewed as projections of some more complex reality."

Dear Dr. Schlafly, I enjoyed your very well written essay. This passage especially resonated with me:

"... some people believe that the mathematical possibilities must be the same as the physical possibilities, even if those possibilities cannot be observed."

To me, a good example of this is "negative pressure" as the cause for expansion. IMHO it can live only in math. I agree with you that mathematics in physics has become divorced from the underlying geometry of creation. In my essay I emphasize the role of space as the container for the Universe and bring up its old, forgotten, paradox, "is space empty or solid?" I find it strange that mathematicians are not bothered that space can be both empty (for matter to move through it) and solid (for light to propagate). I offer a geometrical solution to this old paradox of space, in 4 spatial dimensions, which incidentally removes the mystery out of double slit experiments, to which you often refer in your essay. I would very much appreciate your opinion and feedback on my essay.

Yours was an interesting and informative essay.. As a newcomer to the FQXi community, I feel few of the "community" grade, or even look at, my essay which approaches the problem very realistically, based on an internal view.. Might you look at it, comment if so inclines, and grade it?

Faster Than the Speed of Light, Joao Magueijo: "A missile fired from a plane moves faster than one fired from the ground because the plane's speed adds to the missile's speed. If I throw something forward on a moving train, its speed with respect to the platform is the speed of that object plus that of the train. You might think that the same should happen to light: Light flashed from a train should travel faster. However, what the Michelson-Morley experiments showed was that this was not the case: Light always moves stubbornly at the same speed. This means that if I take a light ray and ask several observers moving with respect to each other to measure the speed of this light ray, they will all agree on the same apparent speed!"

Stephen Hawking: "So if you were traveling in the same direction as the light, you would expect that its speed would appear to be lower, and if you were traveling in the opposite direction to the light, that its speed would appear to be higher. Yet a series of experiments failed to find any evidence for differences in speed due to motion through the ether. The most careful and accurate of these experiments was carried out by Albert Michelson and Edward Morley at the Case Institute in Cleveland, Ohio, in 1887......It was as if light always traveled at the same speed relative to you, no matter how you were moving."

Yet a few Einsteinians teach THE TRUTH: Originally (prior to advancing the ad hoc length contraction hypothesis) the Michelson-Morley experiment unequivocally showed that the speed of light varies as predicted by Newton's emission theory of light:

Relativity and Its Roots, Banesh Hoffmann: "Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether."

http://www.aip.org/history/einstein/essay-einstein-relativity.htm

John Stachel: "An emission theory is perfectly compatible with the relativity principle. Thus, the M-M experiment presented no problem; nor is stellar abberration difficult to explain on this basis."

http://www.philoscience.unibe.ch/documents/kursarchiv/SS07/Norton.pdf

John Norton: "These efforts were long misled by an exaggeration of the importance of one experiment, the Michelson-Morley experiment, even though Einstein later had trouble recalling if he even knew of the experiment prior to his 1905 paper. This one experiment, in isolation, has little force. Its null result happened to be fully compatible with Newton's own emission theory of light. Located in the context of late 19th century electrodynamics when ether-based, wave theories of light predominated, however, it presented a serious problem that exercised the greatest theoretician of the day."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf

John Norton: "In addition to his work as editor of the Einstein papers in finding source material, Stachel assembled the many small clues that reveal Einstein's serious consideration of an emission theory of light; and he gave us the crucial insight that Einstein regarded the Michelson-Morley experiment as evidence for the principle of relativity, whereas later writers almost universally use it as support for the light postulate of special relativity. Even today, this point needs emphasis. The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

My statement is not wrong. The 1801 Young double-slit was the crucial experiment for convincing physicists that light is a wave, and to reject the emission theory. The 1887 Michelson-Morley experiment was crucial for the Lorentz transformations of special relativity. Everyone agrees to this, as far as I know.

Pentcho Valev and Ke Xiao (below) have their own reinterpretations of these experiments. That's great, as this essay contest is a chance to argue that the textbooks are wrong. But even if they are right and the textbooks are wrong, it is still a historical fact that these experiments were crucial experiments for convincing physicists of certain ideas.

Pentcho Valev replied on Sep. 8, 2012 @ 22:59 GMT

Roger,

Since the Michelson-Morley experiment is compatible with Newton's emission theory of light, it by no means showed "that the speed of light was the same in different frames of reference":

http://en.wikipedia.org/wiki/Emission_theory

"Emission theory (also called emitter theory or ballistic theory of light) was a competing theory for the special theory of relativity, explaining the results of the Michelson-Morley experiment. Emission theories obey the principle of relativity by having no preferred frame for light transmission, but say that light is emitted at speed "c" relative to its source instead of applying the invariance postulate. Thus, emitter theory combines electrodynamics and mechanics with a simple Newtonian theory. Although there are still proponents of this theory outside the scientific mainstream, this theory is considered to be conclusively discredited by most scientists. The name most often associated with emission theory is Isaac Newton. In his Corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."

That is, your statement:

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference."

In 1887 Newton's emission theory of light was the only existing theory able to explain the null result of the Michelson-Morley experiment. So your statement:

"The crucial experiment was by Michelson-Morley in 1887, showing that the speed of light was the same in different frames of reference. G. FitzGerald was the first to make the logical deduction from the apparent contradiction, in 1889, by saying, "I would suggest that almost the only hypothesis that can reconcile this opposition is that the length of material bodies changes..."."

is both wrong and misleading, which means that you will be one of the winners in this essay contest.

Pentcho, you are right that the emission theory was the only known explanation in 1887, but it is a historical fact that Lorentz and others eventually convinced everyone that light was a wave subject to the Lorentz transformation. You can argue for emission theories all you want, but can you find any physicist from a century ago who said that emission theory explains light and Michelson-Morley better than Lorentz?

Pentcho Valev replied on Sep. 9, 2012 @ 08:03 GMT

Walther Ritz was the genius, Lorentz and Einstein were dwarfs compared to him. Clever Einsteinians are often secret Ritzians:

https://webspace.utexas.edu/aam829/1/m/Relativity.html

Alberto Martinez: "Does the speed of light depend on the speed of its source? Before formulating his theory of special relativity, Albert Einstein spent a few years trying to formulate a theory in...

Walther Ritz was the genius, Lorentz and Einstein were dwarfs compared to him. Clever Einsteinians are often secret Ritzians:

https://webspace.utexas.edu/aam829/1/m/Relativity.html

Alberto Martinez: "Does the speed of light depend on the speed of its source? Before formulating his theory of special relativity, Albert Einstein spent a few years trying to formulate a theory in which the speed of light depends on its source, just like all material projectiles. Likewise, Walter Ritz outlined such a theory, where none of the peculiar effects of Einstein's relativity would hold. By 1913 most physicists abandoned such efforts, accepting the postulate of the constancy of the speed of light. Yet five decades later all the evidence that had been said to prove that the speed of light is independent of its source had been found to be defective."

Alberto Martinez: "In sum, Einstein rejected the emission hypothesis prior to 1905 not because of any direct empirical evidence against it, but because it seemed to involve too many theoretical and mathematical complications. By contrast, Ritz was impressed by the lack of empirical evidence against the emission hypothesis, and he was not deterred by the mathematical difficulties it involved. It seemed to Ritz far more reasonable to assume, in the interest of the "economy" of scientific concepts, that the speed of light depends on the speed of its source, like any other projectile, rather than to assume or believe, with Einstein, that its speed is independent of the motion of its source even though it is not a wave in a medium; that nothing can go faster than light; that the length and mass of any body varies with its velocity; that there exist no rigid bodies; that duration and simultaneity are relative concepts; that the basic parallelogram law for the addition of velocities is not exactly valid; and so forth. Ritz commented that "it is a curious thing, worthy of remark, that only a few years ago one would have thought it sufficient to refute a theory to show that it entails even one or another of these consequences...."

Jan Lacki: "Ritz had no time to make his theory more elaborate. He died complaining that no one, even in Göttingen, was granting his views sufficient care. His emissionist views were submitted to heavy criticism and experimental tests were later realized to show their inanity. Today, with considerable hindsight, we know the end of the story and how Einstein and Planck's views shaped our contemporary physics. While few would today contest the reality of quanta or turn their back on field theory of elementary processes, it is interesting to know that the criticisms against Ritz's conceptions were shown, since then, often wanting, if not simply incorrect. It is fair to say that if Ritz's emission theory is false, it cannot be as easily dismissed as it was thought in Ritz's times. Be it as it may, Ritz remains in the history of physics as an admirable figure, with a highly original theoretical turn of mind and an impressive command of mathematical methods, making him one of the emblematic theoreticians of his time. In retrospect, if he refused to adhere to the ongoing physics revolutions, he was highly aware of what kind of fundamental problems were at stake, and already this lucidity ranks him among the best."

While I am waiting for a reply by Roger Schlafly, I would like to tell you that in 2007 I tried to publish a paper "A still valid argument by Ritz". I referred to their agreement to disagree. Ritz rejected Einstein's anticipated future.

Given it was a mistake from the very beginning to expect a non-null result from the MMX then both Einstein and Ritz could not find the correct solution. I was guided by Norbert Feist's experiment when I found a quite logical quantitatively matching explanation for the unexpected null result, see my Fig. 5. Any factual objection?

While your views are often at variance with accepted tenets, they largely agree with my own experience, reasoning, and critical analysis of literature.

Inspired by a stunning result of experiments by Feist, Fig. 5 of my essay offers a plausible explanation of why the MMX failed to measure the aether drift. Pentcho did not yet respond.

I have to credit Paul Marmet for making me aware of the key importance of a possible mistake in Potier's correction to Michelson's original calculation: Most likely, this correction was still not yet correct.

Israel Perez claims to reinstate the preferred frame of reference while maintaining Einstein's SR. How do you judge this claim?

Rather than “everything is made from math”, most believe everything can be described by math. There is a difference. Physical reality is described by a subset of the totality of mathematics, and the math to reality map is surjective. The real problem is we look back from the physical reality perspective to mathematics that presents many choices, likely some we may not yet understand or possibly even know about at this time.

The reality of this surjection is some mathematical theories may show initial promise, yet not be fundamental enough to enlighten us on what we do not know. This should not be taken as a condemnation of the concept of using mathematics to describe physical reality. Too few mathematical physicists seem to have the flexibility to keep an open mind on other possibilities, like my shameless plug for my essay. Their intuition and physical religion tenants keep them on the path they are on, and really none of us are capable of demonstrating their efforts are for nothing, whether or not we subscribe to the idea reality has a mathematical characterization. You just have a different religion.

Physicists too often rely on mechanical models that set a particular mathematical path that more often than not more true to the model than it is to actual physical reality. It would be much easier to believe physical reality cannot be mechanically modeled than it is that it cannot be mathematically modeled. Multiple times in your essay you seem to dump on mathematics that could be taken as the result of a poor initial mechanical model and the host of assumptions it provides. You throw the baby out with the bath water.

If you agree that human tradition of entangled co-existence of Physics and Mathematics has sufficient foundation and very long history,then problem is not in belief in pure mathematical reality, but in the search of the new ways of Mathematics-Physics optimization.In my essay I considered such problem as poor mathematical foundations of Relativity, connected with Einstein's complex numbers.R.Penrose made attempt to improve Einstein, and( as is known ) his twistor concept became foundation of String physics. Thus, more or less positive improvements in Relativity mathematics can produce new forms of advanced physics also. I await that some sort of refinements of Einstein's interval technique as well as Einstein-Penrose complex numbers can produce new unexpected developments in theoretical physics and cosmology.

You wrote: "Pentcho, you are right that the emission theory was the only known explanation in 1887, but it is a historical fact that Lorentz and others eventually convinced everyone that light was a wave subject to the Lorentz transformation."

Something similar happened in Orwell's Oceania:

http://www.liferesearchuniversal.com/1984-7

George Orwell: "In the end the Party would announce that two and two made five, and you would have to believe it. It was inevitable that they should make that claim sooner or later: the logic of their position demanded it. Not merely the validity of experience, but the very existence of external reality, was tacitly denied by their philosophy. The heresy of heresies was common sense. And what was terrifying was not that they would kill you for thinking otherwise, but that they might be right. For, after all, how do we know that two and two make four? Or that the force of gravity works? Or that the past is unchangeable? If both the past and the external world exist only in the mind, and if the mind itself is controllable what then?"

Yes "Lorentz and others" did manage to convince everyone that the Michelson-Morley experiment had proved constancy of the speed of light when in fact it had proved variation à la Newton, and that was a tremendously difficult task. The success was so great because relativists were very diligent and constantly exercised themselves in crimestop:

George Orwell: "He set to work to exercise himself in crimestop. He presented himself with propositions - "the Party says the earth is flat", "the party says that ice is heavier than water" - and trained himself in not seeing or not understanding the arguments that contradicted them. It was not easy. It needed great powers of reasoning and improvisation. The arithmetical problems raised, for instance, by such a statement as "two and two make five" were beyond his intellectual grasp. It needed also a sort of athleticism of mind, an ability at one moment to make the most delicate use of logic and at the next to be unconscious of the crudest logical errors. Stupidity was as necessary as intelligence, and as difficult to attain."

I don't know why your essay says "without postulates". You have the biggest postulate of them all -- that there is no physical world and we all live in a big mathematical formula like Tegmark's universe.

Saibal Mitra replied on Sep. 10, 2012 @ 23:16 GMT

It is "without postulates" because (at least in principle) everything should be derived from pure math only. If you assume a physical world then you may have psotulates that can be explained in terms of deeper principles, but there has to be some ultimate set of postulates that are beyond explanation. Everything is then (in principle) explained from thosse fundamental postulates. But if there is no physical world, then there can be no fundamental postulates.

I just read your paper. It took me a while to get to this. I am also not entirely sure what I think of it. I will be honest and say I don’t hold fast to any particular metaphysics or philosophy of science/physics and so forth. I see these at best as hats to be worn at different times.

The relationship between mathematics and physics or science in general will probably never be understood. It is hard to imagine how a mathematical system can function with some concept of ontology, and conversely I am not sure how any theory of science can ever provide empirical content for mathematics. The distant prospect for that might be neurophysiology in the future with some scientific or testable theory of consciousness. For now I am not holding my breath on that.

It is interesting how mathematics used in one particular model system can appear in some other model. Isospin is formally much the same as the old nuclear model, and the AdS/CFT correspondence for quantum gravity, strings and M-theory has appeared in some form with London equations for superconductors. It is then most likely wrong to say that mathematics has nothing to do with physics, and that all of our use of mathematics in physical theory is either some accident or illusion. I also think it is likely the opposite is false as well where people say the physical world is mathematics.

In Penrose’s book “Road to Reality” he starts out with a rather speculative idea of Matter, Mind and Mathematics in a triality system. This is similar to Plato’s idea of physical and perfect forms that are “bridged” by mind, expanded on by Plotius, and frankly the opening of the Gospel of John is basically this same idea. However, this all looks like indemonstrable metaphysics.

You have raised a most relevant question regarding Math and Physics. I have often puzzled why math should be reflected in our measurements of Nature. And have come to the same conclusion as you, I think. This is a 'metaphysical belief' physicists make. I have referenced your essay in my own, “The Metaphysics of Physics”. And further made the argument this belief is only logical if the Laws of Physics are in fact mathematical tautologies. I have shown this to be true, for example, for Planck's Formula of blackbody radiation. This Formula I show is a mathematical truism and not a physical law depending on the existence of 'energy quanta' (see End Note I of my essay).

Through mathematical derivations referenced in my essay I have shown that energy propagates continuously as a wave while it manifests discretely in interactions. And that before manifestation there is 'accumulation of energy'. Such 'loading theory' has also been demonstrated experimentally by Eric Reiter in his essay, ”A Challenge to Quantized Absorption by Experiment and Theory”. I think you will find these essays well worth reading and rating.

I defend my essay on my blog, with postings on Limits of math and A photon is not a math object. Bob Jones has posted some disagreements with me, and I think he gives a good presentation of a mainstream physicist view.

“….A faithful representation of the elementary particles (quarks, leptons, and bosons) is the holy grail of theoretical physics. I believe that there is no such thing, and that it is foolish to look for one…. Arguments for the many-worlds interpretation of quantum mechanics…..the alleged incompatibility between general relativity and quantum mechanics ….. an interpretation of quantum mechanics requiring a conscious observer to collapse the wave function. … Quantum mechanics has a long history of attempts to find faithful mathematical models of reality. All such attempts have failed decisively, both theoretically and experimentally.”

While, the mathematical models describing QM and quantum field theories are extraordinary complex, it is often ignored that such complexity is merely an artifact of the incompleteness and missing physics in QM (as well as GR). Mathematics is just a tool or a language to describe physical reality. Just like a language or tool can be misused, mathematics has been misused to over-extrapolate and over-predict the observed physical reality. Its over-ambitious misuse to compensate for the missing physics (hidden variables), has led to the complexity and non-physicality as evidenced by the current paradoxes of QM and GR. The missing physics, not mathematics, is the root cause of the complexity and non-physicality of the current theories QM and GR. Let us not throw the baby of mathematics with the bath water of the inconsistencies and incompleteness (physical) of QM and GR. At the same time, scientists should not use mathematics to over-extrapolate reality beyond what is observed and physically experienced. The fact however is that complex mathematical pursuits of incredible and non-physical particles, strings, multi-verses, multi-dimensions, quantum gravity, dark matter, dark energy, and so on, have become the dominant mainstream careers in physics/cosmology research and academics today.

My paper demonstrates that a very simple mathematical model of the missing physics (hidden variable) of the well-known spontaneous decay/birth of particles can explain the observed quantum as well as classical behaviors. The model also successfully predicts the observed data at all scales from below Planck scale to beyond cosmological scales. The proposed model not only resolves black hole singularities but also the unresolved paradoxes of physics and cosmology. It also explains the inner workings of QM and eliminates its inconsistencies with relativity. My paper shows that the right physics represented by simple mathematics eliminates the absurdities, complexities, and paradoxes resulting from the misuse of mathematics such as in QM. Mathematics is a useful and credible tool when used in conjunction with the observed or experienced physical reality.

I would greatly appreciate your comments on my paper. You can contact me at avsingh@alum.mit.edu.

I do not know anything about Feist's experiment. Much of modern physics depends on Lorentz's analysis of Michelson-Morley, and of the resulting special relativity. I do not know what it would mean for relativity to be wrong. Likewise with Hilbert space.

Eckard Blumschein replied on Sep. 15, 2012 @ 22:14 GMT

Dear Roger Schlafly,

Feist's relevant measurements are clearly shown in Fig. 7 of the paper I quoted. I quoted Bruhn in order to show how brutally Feist was declared a crank without any attempt to understand his ingenious, carful, and quantitatively convincing measurements. Not even Feist himself gave an acceptable explanation. Having now understood Feist's measurement, I feel ashamed why I did not earlier see that Michelson's reasoning was flawed. Being not the first one who found out that the MMX is inconclusive, I am hoping that my Fig. 5 makes it obvious.

What will it mean for Einstein's relativity to be wrong? Shouldn't it cause you to rethink the chapter "Lessons from relativity" of your essay? In DarkBuzz 2011 you wrote "How Einstein Ruined Physics". Michelson did not like Einstein's relativity while you derived lessons from it. Incidentally, some words in DarkBuzz are almost unreadable for my old eyes.

Maintaining my restricted support for your opinion that mathematical models just tend to approximate the reality I suggest discussing some details at 1364.

It would be exciting if someone devises an experiment that proved relativity wrong. The Faster-than-light neutrino anomaly sure got plenty of attention. But I am not sure it would have anything to do with my essay. We still learned lessons from relativity, even if the theory has to be modified someday.

I need to clarify something before hand to avoid confusion in what I intend to discuss below.

You have in your discussion with Pentcho repeatedly made the mistake of referring to Lorentz contraction (LC) L’ = L/gamma’ as “Lorentz transformation”. No this is worng. Lorentz transformation (LT) is x’ = gamma (x- ut).

I need to clarify something before hand to avoid confusion in what I intend to discuss below.

You have in your discussion with Pentcho repeatedly made the mistake of referring to Lorentz contraction (LC) L’ = L/gamma’ as “Lorentz transformation”. No this is worng. Lorentz transformation (LT) is x’ = gamma (x- ut).

Note: the gamma of LT = 1/(1- u2/c2)1/2 where u is the velocity of the reference frame (in SRT) whereas gamma’ of LC = 1/(1- v2/c2)1/2 where v is the velocity of the particle (relative to the moving frame of velocity u).

Having clarified that misstatement, here is what I wish to discuss:

You wrote: “It would be exciting if someone devises an experiment that proved relativity wrong. ………… But I am not sure it would have anything to do with my essay. We still learned lessons from relativity, even if the theory has to be modified someday”.

Why it has been found difficult to prove SRT wrong is because those trying to prove “Einstein” wrong always pick up the wrong postulate – (1) the constancy of the velocity of light.

At the risk of provoking the wrath of Pentcho, we have to admit that the postulate (1) is right. (Amended as, velocity of light is constant in all directions in a given medium as determined by the refractive index of that medium).

It is the other two postulates that are wrong. (2) Principle of Relativity and (3) Lorentz transformation (LT) [ x’ = gamma (x- ut)].

In Kryakos’ excellent essay http://fqxi.org/community/forum/topic/1341 he has discussed the damage done to physics by young Einstein with his positivist philosophy (but when he realized this, it was too late).

Influenced by the arch-positivist Poincare, (see my essay) Einstein wantonly dumped Galileo’s principle of relativity (which is based on the COMMON MOTION with the unique Local reference frame) and adopted equivalence of all IFR as the second postulate. And he declared that the contradiction between postulates (1) and (2) gets (miraculously) reconciled by adapting LT as the postulate (3).

Now to come to the point:

In Newtonian mechanics (NM) which applies for ‘slow’ motions, displacement of a particle moving at velocity v is given by x = vt. Here space and time are absolute.

For particles moving at near light velocities (in particle accelerator experiments) the displacement is given by x’ = gamma (x- ut). SRT claims that time and space are relative.

So there is a schism in physics (in regard to equation for displacement and also the nature of time and space) which is going unaddressed, by merely making an arbitrary division that “SRT is for fast motion” and “NM is for slow motions”. But the question is never raised “What is the theory that applies to the vast middle ground in between fast and slow motions?”

If you consider particles moving at progressively lesser and lesser velocities (0.9c, 0.8c, 0.7c etc) there is a progressive degeneration of the results conforming to the LT equation. After 0.5c the degeneration becomes much greater. For experiments done of earth, for a velocity of v = 30 k/s the LT equation fully breaks down.

This schism in physics has happened because of the blind adaptation of the LT without discerning its physical basis and deriving it from dynamic principles.

It will be obvious that the schism would disappear if there is an one equation which is applicable to all velocities (slow, medium, fast).

In my essay: http://fqxi.org/community/forum/topic/1549

I not only explain where Einstein went wrong but also following Einstein’s idea of expanding the thermodynamic approach to whole of physics I also have developed the general equation of motion

x’ = gamma vt(1- u/c) --------------(1)

Note: This equation (1) tends to LT -----(2) at near light velocities where v/c tends to 1; and to x = vt -----(3) when v/c tends to zero.

We do not need any new experiments to verify the validity of this equation. Experiments have already been done. If we take the results of all the particle accelerator experiments done in the last hundred years and make a computer analysis, it will show that the results conform to the above equation (1).

Your point of view that what is perceived to be ‘mathematical reality’ is not ‘physical reality’ would seem to be confirmed by the fact that LT has an inbuilt error which looms large when the velocities decline.

I would like you to read my paper and give your comments. (For clarity of diagrams I have also attached essay in MS Word format

Are you claiming that there is experimental evidence that the relativity principle is wrong? Or that the Lorentz transformation is wrong? If so, how do you explain all the experiments that have confirmed relativity?

Eckard Blumschein replied on Sep. 16, 2012 @ 13:09 GMT

Dear all,

How can the many putative confirmations of SR be explained? This is perhaps as troublesome as to disprove the many proofs for the existence of God. My Refs. 5 and 6 list some of those who are dealing with this matter. As Viray Fernando mentioned, most objections against Einstein's relativity tried to put the postulate of constant c in question. When proponents of Einstein's relativity Emission theories disproved emission theories then this was celebrated in public as confirmation of Einstein, for instance in the case of OPERA. The postulate of relativity seems to be so natural and Galileo's relativity is not just correct but also plausible to everybody. Virtually everybody followed Lorentz or Einstein because the MMX seemed to be compelling and Maxwell's equations were not covariant.

You wrote: "...how do you explain all the experiments that have confirmed relativity?"

At least the Adams-Eddington 1925 glorious confirmation of "Einstein redshift" is easy to explain, Roger. One word is enough: FRAUD.

Open Questions Regarding the 1925 Measurement of the Gravitational Redshift of Sirius B, Jay B. Holberg Univ. of Arizona: "In January 1924 Arthur Eddington wrote to Walter S. Adams at the Mt. Wilson Observatory suggesting a measurement of the "Einstein shift" in Sirius B and providing an estimate of its magnitude. Adams' 1925 published results agreed remarkably well with Eddington's estimate. Initially this achievement was hailed as the third empirical test of General Relativity (after Mercury's anomalous perihelion advance and the 1919 measurement of the deflection of starlight). IT HAS BEEN KNOWN FOR SOME TIME THAT BOTH EDDINGTON'S ESTIMATE AND ADAMS' MEASUREMENT UNDERESTIMATED THE TRUE SIRIUS B GRAVITATIONAL REDSHIFT BY A FACTOR OF FOUR."

"...Eddington asked Adams to attempt the measurement. (...) ...Adams reported an average differential redshift of nineteen kilometers per second, very nearly the predicted gravitational redshift. Eddington was delighted with the result... (...) In 1928 Joseph Moore at the Lick Observatory measured differences between the redshifts of Sirius and Sirius B... (...) ...the average was nineteen kilometers per second, precisely what Adams had reported. (...) More seriously damaging to the reputation of Adams and Moore is the measurement in the 1960s at Mount Wilson by Jesse Greenstein, J.Oke, and H.Shipman. They found a differential redshift for Sirius B of roughly eighty kilometers per second."

My essay is not about the evidence for and against relativity. I do not doubt that some people have been misled by bad experiments, but that is off-topic. There are many other experiments.

Eckard Blumschein replied on Sep. 16, 2012 @ 21:10 GMT

Dear Roger Schlafly,

Wouldn't providing any evidence be OK because wrong evidence can be refuted? The welcome rather than suicidal argument "there are many other experiments" indicates either blind or pretended trust in the a mandatory belief. You were courageous enough as to write "Einstein Ruined Physics". Isn't such utterance premature without the clarification that Einstein's main theory is wrong? If you yourself were mislead by a bad experiment, is this off-topic?

Didn't you call Einstein overestimated? Even if Einstein's relativity is wrong I will not primarily blame himself for that. Einstein was fostered by Max Planck, and his ideas on relativity were not much different from those by Lorentz and Poincaré, and they altogether were misled by Michelson's experiment.

Since you have a PhD in mathematics, I would appreciate your opinion at least concerning my Figs. 1 to 4. You wrote "some irrational numbers are so complicated that no computer can generate their decimal expansion". Can you please exemplify this?

I dislike your style of argumentation. You do not even try to explain "How Einstein Ruined Physics" with his relativity, and I am beginning to doubt that your somewhat nihilistic rather than positivist essay will lead to anything useful.

You wrote:

(i) "There are uncountably many irrational numbers, but only countably many computer programs"

(ii) "The irrationals are also needed for a physical reality."

(iii) "Some [irrational numbers] are not even definable in ZFC". Are these going to be allowed as part of the strict mathematical definition of an electron? No one can answer that."

While I agree on that computer programs are just parts (in Euclidean sense) of the reality, I see no compelling reason to abandon the experience of an open, i.e. potentially infinite universe.

My answer to (iii) is given with my Fig. 4 and questions the notion "strict mathematical definition".

I asked for an exemplification of (iii) which is perhaps not available.

What about publication, doesn't the public FQXi contest offer a more competent and much faster scrutiny for really important arguments than the system of two anonymous referees? You might feel challenged.

Eckard, I am here to discuss the ideas in my essay. I did not express any opinion on whether the universe is finite or infinite. This essay contest gives you a chance to argue that relativity is wrong, but that is not my argument.

Eckard Blumschein replied on Sep. 17, 2012 @ 14:06 GMT

Robert,

Doesn't Einstein's and Hilbert's view imply the Block universe and the Schwarzschild solution? I didn't primarily intend to refute Einstein's relativity. Starting from obvious distinction between past and future, I looked for a reasonable solution to the puzzles and confirmed logical inconsistencies in set theory and in what has been concluded from MMX which were already found by many many others. I hope, the plausible alternative I am trying to offer will persuade and unite a sufficient number of opponents. So far, many in this minority prefer neo-Lorentzian interpretations or emission theories.

Incidentally, I would like to warn about a faithful representation of nature. Faith denotes either a strong belief in a religion, no matter whether Buddhism, Christianity, Set Theory or Einstein Relativity or loyalty to it. Perhaps you meant trustworthy, something I can agree on because it does not exclude the treasure of possible mistakes to be found.

I do not agree with the thesis of your essay. Deny the possibility of a mathematical description of reality is deny the possibility to find general objective rules to describe nature. This would be the end of natural philosophy and science of Pythagoras and Galileo. This means to give up with the effort to understand nature. It is reductive to say that the scientific method is...

I do not agree with the thesis of your essay. Deny the possibility of a mathematical description of reality is deny the possibility to find general objective rules to describe nature. This would be the end of natural philosophy and science of Pythagoras and Galileo. This means to give up with the effort to understand nature. It is reductive to say that the scientific method is all wrong without giving alternative frameworks or proposing new assumptions. You use the complexity of quantum mechanics to claim that nature has no faithful mathematical description, but quantum mechanics is the demonstration that mathematics works by far better than our physical intuition. The amazing accuracy of the predictions of the anomalous magnetic momentum of the electron is an absolute demonstration of the power and correctness of our mathematical description of quantum mechanics. The problem of quantum mechanics is that we have not grasped the underlying physical meaning of QM, i.e. the physical meaning or geometrical description of QM. Copernicus's revolution and Kepler have taught us that a geometrical or mathematical problem apparently impossible or extremely difficult to formalize in simple roles, if approached with the correct physical assumption, e.g. by using the Sun as origin of the coordinates of the system, suddenly simplifies in an elegant mathematical equations or geometrical elements (try to describe planet motions using the Earth as origin of your coordinates, the equations are so complex that the underlying symmetries are completely hidden). A physics hypothesis is true as long it describe consistently our observations.

In my essay Elementary Time Cycles I discuss how all the fundamental aspects of quantum mechanics and relativity are conciliated in an elegant mathematical form. This has the same form of the system which originated mathematics with Pythagoras and it is at the base of the all modern theory of physics: this is the mathematical description of a vibrating string with all its harmonics. In my papers, published in leading scientific journals, I show with rigorous mathematical demonstrations, certified with peer-review in the better scientific tradition, that the "missing link" for a consistent description of the most fundamental aspect of quantum world is an assumption of intrinsic periodicity of isolated systems, as implicit suggested nearly a century ago by the fathers of quantum mechanics (de Broglie, Bohr, Sommerfeld, Schrodinger, Fermi, Dirac, ...). The mathematics is correct, and this is easy to check. Nevertheless in some cases I had the funny comment that my results are (a long series of) "mathematical coincidences". My question is: What is not a mathematical coincidence in physics?. A mathematical coincidence, if exists, is only something that works mathematically but it is not well understood conceptually.

An answer to a problem should be simple, otherwise it is only a complication. We should always remember Galielo's lesson: "Io stimo piu' un vero, benche' di cosa leggiera, che al disputar lungamente delle massime questioni senza conseguir verita' nissuna" [I deem it of more value to find out a truth about however simple thing than to engage in long disputes about the greatest questions without achieving any truth], Galileo Galilei

Why believe old dead guys like Pythagoras and Galileo when we have so much more knowledge than they did? Yes, geometry has done wonders in the past, but we should at least consider the possibility that it will not solve everything.

You have posed 3 questions to me. Pending providing detailed answers to all in a later post, I will take up the 3rd question for now.

You asked:

“If so (i.e. if Lorentz transformation is wrong), how do you explain all the experiments that have confirmed relativity?”

I suppose what you mean is: “how do you explain all the experiments that have confirmed Lorentz transformation?”.

Lorentz transformation in the sense Einstein means it, is not only about the displacement x’, it must also hold equally true for time t’.

I would like to ask whether you know of any experiment that has confirmed LT equation for time t’ = t(1 – ux/c2).gamma?

In accelerator experiments, if the observer measures the displacement as x’ = gamma (x –ut) relative to the lab frame (using its ‘meter stick’), and considers this confirms LT (displacement), then corresponding to that, the time measured relative to the lab frame clock should be t’ = t(1 – ux/c2).gamma. Is this the case?

You cannot say that when x’ is measured relative to the lab frame, t’ is a measurement that would be true relative to a frame co-moving with the particle. Both x’ and t’ must be measurements made with respect to the meter stick and the clock of same frame.

The Achilles heel of SRT is what is believed to be its forte – the LT’s.

SRT claims laws of physics are the same in all IFR and then in the same breath wants us to believe that a particle will move according to classical laws at slow velocities and will conform to Lorentz transformations at near light velocities in a given frame.

Should not laws of physics be the same for all velocities (in a given frame)? That is, should it not be the case that there has to be one equation covering all velocities?

Actually it is very easy to develop such an equation logically which holds for all velocities. The logic is this: If the displacement x’ = gamma(x –ut) when velocity of the particle v tends to c, i.e. v/c tends to 1, then the general equation for displacement will be given for all velocities v by

x” = gamma.v/c(x –ut)

The implication of this equation is that as ratio v/c becomes smaller and smaller than 1, the results will be deficient from the predictions of SRT by the term

a = x’(1 – v/c)

The tasks then is

(1) to derive this equation for x” from dynamical principles

(2) Have the general equation verified against results of experiments for particles moving at various velocities performed in the last 100 years by computer analysis. This will be the ‘experimentum crucis’ that will decide on the fate of SRT.

See: A Treatise on Foundational Problems of Physics , I have derived this equation from first principles on a dynamic basis.

BTW I pointed out in my previous post to you that you are confusing between Lorentz contraction and Lorentz transformation. I notice that you made no comments about that. When no attention is paid for conceptual clarity, it is quite possible nature may appear not to have any faithful representations.

Wigner gives examples of mathematical formulas being used to make predictions that agreed with experiment. I have no quarrel with that.

Hoang cao Hai wrote on Sep. 19, 2012 @ 15:00 GMT

Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

"Quantum mechanics is the first theory to truly take the cave allegory seriously. It has a theory for how observations correspond to projections, without ever trying to explain what is outside the cave."

Nice essay but I have some remarks: the problem of faithful represantation of nature in math would be well-defined under the supposition that mathematics itself is unchanged and fixed. In fact, the development of theories of physics makes the mathematics is developing and changing. Also mathematics itself changes and evolves. If we assume that mathematics is constant and corresponds to fixed understanding, even describing mathematics by mathematics would not give coherent picture and it seems that it would not exist a faithful represantation of mathematics in mathematics. Let me mention model theory which allows for changing reals or naturals as different models. When facing such change from the point of view of 'older' mathematics it is an absurd. Another example is 2-valued logic. Intuitionistic set theory, or some other logics, might be seen as an absurdity from the point of view of Aristotle logic. Another example - non-Euclidean geometries - from the point of view of 5-th Euclid axiom these are absurdities. However, they appeared subsequently to be physically valid. Similarily intuitionistic logic etc., etc.... So, the problems with finding best mathematical representation for physical world is also the problem with developing suitable mathematics. Certainly, this still be a represantation or model rather than a nature itsel. As so, this representation differs from the physical reality. Obviously, one can represent nature by other means, like art works, but this suffers from the individuality and leads to difficulty with representing repetitive results.

In my essay I deal with such changing mathematical perspective as suitable to physics: What if Natural Numbers Are Not Constant? http://fqxi.org/community/forum/topic/1443

Mathematics is defined by what is provable in ZFC set theory. Non-euclidean geometry, nonstandard reals, etc. are all definable in ZFC. Yes, there are other logics, such as intuitionist logic, but it is going to be a whole lot harder to find some representation of nature in intuitionist logic.

Jerzy Krol replied on Sep. 23, 2012 @ 21:19 GMT

In fact, it is not so -

1. only 1-st order properties are expressible and provable in ZFC. Topology, smoothness etc. require higher (2nd) order languages. Also, Paul Benioff showed in 1976 that the mathematics of ZFC is not powerful enough for a formalism of quantum mechanics.

2. intuitionistic logic is 'wider' (or weaker) than the classical, so it can interpret (in the limit) the same what classical logic can do.

3. however, the above two points are merely illustrations for the main point of my previous post which you did not adress at all.

Topology and smoothness can all be analyzed in first order logic (ZFC). No, 2nd order languages are not necessary. I am not familiar with that Benioff paper. Do you have a link?

Author Roger Schlafly replied on Sep. 24, 2012 @ 04:04 GMT

I found this 1976 Benioff abstract and this. He seems to have tried to show that the choice of ZFC model can have some physical significance. I am not sure this has much relevance to our discussion here.

Do you state that there are no 2-nd order properties of any topological or smooth space? Or more generally, maybe there are no 2-nd order properties of any mathematical structure which would not be a 1-st order? In that case we indeed need not 2-nd order languages at all. Even, the 1-st order structure of real line is extremely complicated which becomes tame when higher order is switched on (cf. 600pp book of Bartoszynski - 'On the structure of real line'). Other, but related, thing: models of 1-st order theories, like PA, or ZFC, are completely different than models of 2-nd order arithmetics or set theory. If the theories were equivalent (or the same) their models either. I am not saying that one can not speak about 1-st order properties of topological or smooth spaces. In that case, certainly, we do not need higher order languages.

The relevance of Benioff work to our discussion is the following: Benioff showed that there exists a model (rather generic, minimal) of ZFC which is not 'carrier for mathematics of QM'. Similarly, no forcing extension of the model represent randomness as in QM. This means that provability within ZFC does not suffice for describing mathematics of physics (everything provable in ZFC holds true in every model of ZFC). These results are about power of provability of ZFC which is too weak for mathematics of physics.

Again, the above points were not the main thing which i tried to ask you to comment in my 1st post. This was rather the supposition about the constant and well known structure of mathematics, which if one assumes so, gives rise to the difficulties and inconsistencies even in the case of interpreting mathematics within mathematics. So, building the interpretation of physics in such understood, non-developing and constant mathematics is again not faithfull by the same reasons.

Jerzy, I do not accept your view of mathematics as changing so much. ZFC is a suitable axiomatization of math, and it has not changed in decades.

There is some merit to 2nd order logic, but it is not necessary for topology or smooth space. 1st order ZFC works fine. I guess you agree that we do not need higher order languages.

I haven't seen Benioff's papers, but I do not believe that he proved that ZFC was too weak for QM because some ZFC models do not represent randomness as need in QM. That does not make any sense to me. Everything I know about the mathematical structures for QM can be done in ZFC. His abstract says, "if a strong definition of randomness is used". Maybe his problem is with his own peculiar definition of randomness.

Jerzy Krol replied on Sep. 25, 2012 @ 12:27 GMT

Thanks Roger, but if you accept only 1-st order theories you have to accept the consequences of such choice; it is not just matter of taste; let me recall again the pletora of models appearing just in 1-st order and disappearing in highers, etc. I advice, and would be grateful in fact, if you take a look into my essay which is precisely about 1-st order math having strange consequences in physics....

Thanks Roger, but if you accept only 1-st order theories you have to accept the consequences of such choice; it is not just matter of taste; let me recall again the pletora of models appearing just in 1-st order and disappearing in highers, etc. I advice, and would be grateful in fact, if you take a look into my essay which is precisely about 1-st order math having strange consequences in physics. 1-st order mathematics is one realm, 2nd and higher are different realms - this is the fact not just a choice. We can consider topological and smooth spaces in ZFC but as far as their 1-st order properties are considered (again, Bartoszynski book). In particular this means that we can not quantifie over open subsets etc. Due to this discripancy there are non-standard (Robinson's) models of reals in 1st order which become isomorphic in 2nd., simply because we do not see (can not express) their isomorphism in 1st order, etc.

Considering ZFC as a non-variable and absolute base fo rmathematics is what generally people say about foundations of math. But the development of category theory and topoi in particular changed and changes that situation. Even in physics we use very informal, arbitrary high level reasonings which hardly become 1-st order. Only from that point of view the language of physics is non-compatible with 1-st order mathematics and can not be reduced. But something more fundamental happens: when we assume that mathematics (and its foundations) is unchanged and absolute and does not undergo development and change (which it does, anyway, is the fact), is sufficient for having non-faithful representations of math in math itself. Because of that it is not much surprise to have non-faithful representation of physics, based on math, in math. From practical purposes it is very convenient and easy to fix developing math and contain it in well-defined tame system, but sooner-or-later such action will fail due to the error of such simplification. I know there is many things which should be discussed here, probably too many for such forum. Thanks that your essay allows for such discussion.

Regarding Benioff's result I could just repeat what I told in the earlier post.

I agree with Jerzy Krol and would like to add my own arguments. Given mathematics is defined by what is provable in ZFC set theory, then it seems to be unlikely to escape from this prison. Those like me who got aware of brutally ignored inconsistencies may hope for the insight of physicists that some puzzles can only be resolved with corrected mathematical foundations. I gave some examples of admittedly marginal inconsistencies in 833 .

ZFC indirectly assumes trichotomy. I learned from Fraenkel 1923 that trichotomy does not include the fourth logically possible relation between two objects.

If mathematics is defined by what is provable in ZFC set theory, then ZFC set theory is not mathematics.

Interesting thoughts. If not mathematical, what is the alternative for a working assumption in science? The positivist view doesn't tell me much about the impact of adopting a non-mathematical position (by the way, paradoxically I think the positivist view in philosophy is your opposite view). It seems that assuming a non-mathematical position would lead to either inoperativeness or would have no impact in the practice of science.

On the other hand, quoting you "It seems unlikely that mathematical structures would be suitable for a true physical reality." I wonder if you wouldn't buy it if "mathematical structures" are replaced by "computer programs". I guess, however, that you see computer programs as mathematical structures. I don't, I think they are fundamentally different, the latter come with their implementation, the former don't, hence it may be easier to accept that something is a computer program rather than a mathematical structure even when a computer program can be mathematically described (and that is the difference, one is a description the other is a prescription).

Yes, computer programs are mathematical structures. If they can be programmed on a Turing machine, then they are reducible to pure math.

Mathematics is tremendously useful for doing science. No one can deny that. But my working assumption is that physics and math are two different things.

Hoang cao Hai wrote on Sep. 24, 2012 @ 02:49 GMT

Nothing more accurate!

Mathematics is just a tool to do the job is directed by the thinking of intellectual.

It only accepted to manifest when a result of the thinking of intellectual was accepted.

Correct is we are doing the opposite: hurry to accepted it (turn it into a basic law in constitution - unwritten - of Science), while there is still a mountain of questions but it does not have the solution response - on over century.

If acceptance to used a tool (as Mathematics) is the mainstream of our Science,certainly is our intellectual achievements will be determined by turning the roulette or will is the series products of an automated production line.

Too incredibly bizarre, when we set up the equation or formula to calculate in order to determine what we imagined, but can not the specific and detailed definitions for them, even when it is incongruous with the reality of nature.

E = m.c2 can calculate the energy of a potato or a loaf of bread?

You have written an "ultimatum" on behalf of all those who recognize that there are a lot of "assuming our basic foundation is wrong" and Mathematical was to "squared" for this the wrong.

(You posed questions to me. I am drawing your attention to the answer I gave)

You have posed 3 questions to me. Pending providing detailed answers to all in a later post, I will take up the 3rd question for now.

You asked:

“If so (i.e. if Lorentz transformation is wrong), how do you explain all the experiments that have confirmed relativity?”

I suppose what you mean is: “how do you explain all the experiments that have confirmed Lorentz transformation?”.

Lorentz transformation in the sense Einstein means it, is not only about the displacement x’, it must also hold equally true for time t’.

I would like to ask whether you know of any experiment that has confirmed LT equation for time t’ = t(1 – ux/c2).gamma?

In accelerator experiments, if the observer measures the displacement as x’ = gamma (x –ut) relative to the lab frame (using its ‘meter stick’), and considers this confirms LT (displacement), then corresponding to that, the time measured relative to the lab frame clock should be t’ = t(1 – ux/c2).gamma. Is this the case?

You cannot say that when x’ is measured relative to the lab frame, t’ is a measurement that would be true relative to a frame co-moving with the particle. Both x’ and t’ must be measurements made with respect to the meter stick and the clock of same frame.

The Achilles heel of SRT is what is believed to be its forte – the LT’s.

SRT claims laws of physics are the same in all IFR and then in the same breath wants us to believe that a particle will move according to classical laws at slow velocities and will conform to Lorentz transformations at near light velocities in a given frame.

Should not laws of physics be the same for all velocities (in a given frame)? That is, should it not be the case that there has to be one equation covering all velocities?

Actually it is very easy to develop such an equation logically which holds for all velocities. The logic is this: If the displacement x’ = gamma(x –ut) when velocity of the particle v tends to c, i.e. v/c tends to 1, then the general equation for displacement will be given for all velocities v by

x” = gamma.v/c(x –ut)

The implication of this equation is that as ratio v/c becomes smaller and smaller than 1, the results will be deficient from the predictions of SRT by the term

a = x’(1 – v/c)

The tasks then is

(1) to derive this equation for x” from dynamical principles

(2) Have the general equation verified against results of experiments for particles moving at various velocities performed in the last 100 years by computer analysis. This will be the ‘experimentum crucis’ that will decide on the fate of SRT.

See: A Treatise on Foundational Problems of Physics (attached) , I have derived this equation from first principles on a dynamic basis.

BTW I pointed out in my previous post to you that you are confusing between Lorentz contraction and Lorentz transformation. I notice that you made no comments about that. When no attention is paid for conceptual clarity, it is quite possible nature may appear not to have any faithful representations.

Viraj, you did not answer my questions. If you think that relativity is wrong, go ahead and post your evidence and reasoning in your essay and your forum. We will all be excited if you show that relativity is wrong. But the issue has very little to do with my essay.

Viraj Fernando replied on Sep. 25, 2012 @ 19:51 GMT

Roger,

You wrote: "you did not answer my questionS" (in plural to cover your lie). I answered one, and expected your response to answer the other two as stated. Since you make the allegation that I did not answer your questionS (in plural), I will answer the remaining two as well.

This institute has the name FOUNDAMENTAL .and you Mr Tegmark you say that the uniqueness is not essential. the multiverses are not rational Mr Tegamrk.and your responsability is to be rational for the well of this institute.If you have a lack of ideas, so insert the multispheres !!! It is what the probelm, you fear for your place or what...

This institute has the name FOUNDAMENTAL .and you Mr Tegmark you say that the uniqueness is not essential. the multiverses are not rational Mr Tegamrk.and your responsability is to be rational for the well of this institute.If you have a lack of ideas, so insert the multispheres !!! It is what the probelm, you fear for your place or what ??? personally a platfrom like this one merits rational thinkers like Mr Wilsczec for example or Mr Penrose. Or Mr Witten but your parallel universes frankly.parrallelizable spheres, no but frankly Mr Tegamrk, you need at this point investments. I will be a better director with Mr Penrose than you with these paralleizations where the foundamentals loose their meaning. The mathematical hypothesis is interesting but with your parallel universes, all is false just because you confound the uniqueness.

an institute like this one has a pure universal responsability. you cannot teach pseudo sciences.I am sorry to tell you it but your parallel Universe cannot be a reality. The real interest is to focus on our pure universal 3D sphere and its intrinsic laws.The technologies can be optimized in understanding these laws.The maths are a tool, so what do you do with the maths???? The universal domain is essential. It is a foundamental the uniqueness. it is the reason why the name UNIverse is inserted.If you spoke about the subjectivity and the extrapolations of humans where all people has its own universe in its perception. There I can agree, but what are these multiverses of parallelizations ??? It is not rational. I can understand that you like your reasoning.But frankly you cannot teach that at school and university. You confound the theory of informations, with the mathematical extrapolations and the pure deterministic realistic Universe. So it implies a lot of confusions. I aminsisting on the fact that you cannot teach that to students. It is not possible. They must learn the foundamentals and not the irrationalities. It is evident in fact. I beleive that you must be rational. and you Mr Aguirre, you also you are in the publicity of multiverse.Why you do not say the multispheres. Frankly if you continue in this road, so change the name of your institute and name it, the subjective questions and hypothesis Institute. Because there if you want really having intresting funds, change of sciences. You are not going to be accepted for the rational part.But it is just a suggestion.

Multispheres , it is not bad like idea.I have an idea objectivity vs subjectivity

Unisphere vs Multispheres.

Thesis vs antithesis

like that you shall have funds, it is cool no? you like monney, see so the potential ahahah

I suppose you agree that Physics is Experimental Science, correspondingly, if "The faithful mathematical representation hypothesis is such an

assumption, and it might be completely wrong", then as physicist you must have experiments in order to prove it.

Let us consider thought experiment. Following your ( very popular ) opinion, because Nature has no the faithful mathematical representation, then such sort of mathematical claim as " Nature uses equation of the type x^2+y^2=z^2 but Nature cannot use equation of the type x^3+y^3=z^3 " is wrong.

Please, can you test it, may be you can find counter-example (for Fermat theorem ) in Nature which you know better?

I don't know how to experimentally prove that nature has no faithful mathematical representation. If two formulas make different predictions, then an experiment could show that one is right and one is wrong. But even if both are wrong, there could be a third formula that is exact.

The best experimental evidence comes from quantum mechanics, and the failure of hidden variable models. False intuition about mathematical representations had led people to propose hidden variable models, but these have all been disproved by experiment.

Frank Martin DiMeglio wrote on Sep. 29, 2012 @ 17:07 GMT

Roger, here is fundamental proof of the limits of mathematics, including why mathematics will never fundamentally and generally unify or describe physics.

Ultimate unification in physics combines, balances, and includes opposites. MATHEMATICS CANNOT COMBINE, BALANCE, AND INCLUDE OPPOSITES.

In keeping with the above, fundamental gravitational and inertial equivalency and balancing (both at half strength force) fundamentally proves and demonstrates F=ma. A MOST IMPORTANT POINT -- DO YOU AGREE? (As acceleration is fundamentally balanced and averaged as well.)

Accordingly (and most importantly), there are serious, FUNDAMENTAL, and ultimate limits to physical understanding, physical prediction, and physical description (including mathematical). Do you agree?

If Nature has lovely mathematical representations,for example, Nature likes Fermat theorem, then such consequence of Fermat theorem as an impossibility of x^3+y^3=z^3 must be naturally accepted in any human logical system of axioms, hence, it is sufficient to find MERELY physical or mathematical counter-example in order to destroy all modern Number theory of believers in "pure mathematical reality ".Thus, philosophical principle :

"If two formulas make different predictions, then an experiment could show that one is right and one is wrong. But even if both are wrong, there could be a third formula that is exact " cannot be applied in this case.

2 You ,unfortunately, wrongly suggest that " The best experimental evidence comes from quantum mechanics, and the failure of hidden variable models. False intuition about mathematical representations had led people to propose hidden variable models, but these have all been disproved by experiment."

In famous article by J.Bell " on measurements " Bell showed that so-called "hidden variables" are not classical integers of classical number theory, but just classical physics variables.As is known,Bell inequality is connected with an existence of complex numbers in Nature and his four Bell's states are solutions of eqation of the type z^2 = x + yi...

Bell showed that certain plausible hidden variable theories could be experimentally tested. All such experiments have disproved the hidden variable theories. See Bell test experiments.

Joy Christian replied on Oct. 1, 2012 @ 16:11 GMT

"All such experiments have disproved the hidden variable theories."

And I have disproved Bell's claim that "no physical theory which is realistic as well as local [in the senses specified by EPR and Bell] can reproduce all of the statistical predictions of quantum mechanics."

Your assertion is based on a prevalent but unjustified belief system, not on a rational and unbiased scientific investigation.

The mistakes, misconceptions, and straw-man arguments in all of the so-called rebuttals of my Disproof you have linked, have been systematically exposed and debunked, not only by me, but also by several other people, here, here, here, and in the attached pdf document. In essence, all arguments against my disproof so far have only been arguments from prejudice and ignorance, not science.

Nevertheless, if you point out to me just a single valid argument from any of these so-called rebuttals, I will reconsider my opinion that your assertion above is based on a prevalent but unjustified belief system, not on a rational and unbiased scientific investigation.

I thought Joy had quite convincingly disproved Gill (bivector error etc.) and previous attempts at falsification. http://arxiv.org/pdf/1203.2529.pdf Are there any later attempts not refuted?

I'm also interested in your views on Tom's excellent essay (and if you have time, mine too of course!) There are also some other excellent papers with disproof's or Bells theorem here which I haven't yet noticed you comment on, i.e. Sycamore and McEachern etc, including from information theory. Your response to those would be interesting.

I didn't recall your own proposition relied at all on Bell. Do advise if that's incorrect.

No. All such experiments (being quantum experiments) indicate that the predictions of QM are probably correct. Those experiments do not disprove hidden variable theories. It is false science to say that they do. It is also false science to say that the quantum experiments prove that QM is complete. They do not prove that.

I agree with Fred that the experiments simply prove that quantum mechanics makes the correct predictions. They do *NOT* prove that Bell is correct or that quantum mechanics is complete. It is much more complicated than that.

Yes, Manin is a smart guy with many interesting things to say. Did you see anything to lead you to believe that he would agree or disagree with my essay?

Frank Martin DiMeglio wrote on Oct. 1, 2012 @ 18:08 GMT

Roger. Your reply to my prior post please. Also, the objective is to have a seamless and undivided whole, as ultimate unification in physics combines, balances, and includes opposites. MATHEMATICS CANNOT COMBINE, BALANCE, AND INCLUDE OPPOSITES.

Time is ultimately dependent upon the integrated and interactive extensiveness of being, thought, and experience (and space). Time requires gravity. In the absence of gravity, we are literally out of touch with reality. Another physical fact that mathematics fails at.

The key here is to describe thought [fundamentally and generally] in conjunction with/relation to physics, force/energy, and sensory experience (in general). My essay does this. Mathematics cannot do this.

The reductionist and mathematical approaches are ultimately doomed in conjunction with the following:

The self represents, forms, and experiences a comprehensive approximation of experience in general by combining conscious and unconscious experience. (A great fact of physics too.)

Physically speaking,John Bell showed that it was indeed possible to realize the EPR-experiment, when the two particles are emitted with definite spin directions, which are locally fixed at the decay. These directions, according to Bell,however, might be unknown to the experimentalist. He then showed that if we measure the spin of particle 1(natural number,sorry)along one direction, and the spin of particle 2 along another direction, the results will be correlated. For instance, if we measure the spin of both particles along the same direction, particle 2 will always have the spin down when particle 1 has the spin up.

Thus, they are correlated (or rather, anti-correlated).But if the spins are measured along different directions, the correlation will decrease.(Since Bell's discovery, a number of experimental tests have been performed successfully [by J Clauser and S Freedman (1972), A Aspect, J. Dalibard, and G Roger (1982), and G Weihs, Ch Simon, T Jennewein, H Weinfurter, and A Zeilinger (1998)],etc )...

Mathematically speaking, however, Bell' Nature has faithful mathematical representations in the form of complex numbers which can exist only in Hilbert complex vector space. Thus, iff somebody has alternative more advanced mathematics as well as he knows better Nature's own mathematical taste,it is naturally to ask to prove such sort of claim.Technically and experimentally.

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is

and

was the quantity of people which gave you ratings. Then you have

of points. After it anyone give you

of points so you have

of points and

is the common quantity of the people which gave you ratings. At the same time you will have

of points. From here, if you want to be R2 > R1 there must be:

or

or

In other words if you want to increase rating of anyone you must give him more points

then the participant`s rating

was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

I really like your essay even though I don't necessarily agree with all you say. To me, these are the important and interesting issues: what reality do the mathematical equations of physics represent; and what reality do the numbers found in nature represent.